100% personal bike use

Let's get clear on the premis. That is all personal transport becomes bike based, or pedal powered if you're a unicycle or recliner fan. Morons. So the obvious exceptions are commercial vehicles, that is ambulances, some police cars and such. Not taxi's though too easy to overcome that little difficulty.
So now a commercial vehicle is also not (?) a car you use to drive to work. Just like you don't get a tax break on it, so too is it not a commercial vehicle.
Public transport may also be excluded.
How could it work?

Well shopping comes as the first major obstacle. How to get around it? well it would be hardest on people doing the most shopping for many people. This though suggests the simple technology solution of online shopping, it would no doubt be far more economical to just order up in totallity what you want from the store and have its commercial freighter drop it off not just for your family, but your entire neighbourhood, Postal service already provides the infrastructure.
Less practical is for guys like me, buying for one person, often for only one or two nights meals. Nutritionally this is beneficial, particularly if I buy local, but the walk is a bit of a pain. I know its entirely possible though because this was how I lived for 3 years. Occasioanally on the way home I bought dinner provisions and hung them from my handlebars, but the green bags are terryfying to watch go through my spokes and the green bags, both annoying and dangerous to the food inside.
The simple answer is to put a rack or basket over the back wheel to chuck food in, this is the sort of dorky-practical solution I will go out of my way to avoid.
But non-the-less to the more frequent smaller purchase death of the weekly shop, this does overcome the difficulty of shopping for most people. I will still walk because I don't want anything so ungainly as a pack rack in any way associated with my explodinator. But fact is if shopping bothers you and the suburban walk seems too far, get a pack rack.
And that's the other solution, shop for less, more frequently, and just walk it. It bodes to a greater structural solution, which is relocating supermarkets to accomodate for people's limited reach. Maybe a return to the General Store, though nothing as stupid as the local owned general store. One would hope that fresh produce got picked ripe and thus was local aswell but a small sufficient general store should suffice for most buying needs in the hood, within walking distance and shit, but maybe is a national franchise with the buying power of say Coles or Woolworths.
For those that like the big markets like Vic Markets, then public transport is the solution, or otherwise fit some trailer to your bike or get some god awful three wheeler then stock up. If you need a big 4 x 4 car now with the back seat put down to buy all your groceries you need to sell some of your children to some organ harvesters.

Hygene, suppose you are going to a dinner party or work or whatever? this is simple, where a good cycling jersey and shorts then after your commute ride or cross town journey, simply make use of a room to change. studies show 85% of regular bike commuters don't bother to have a shower on arriving, changing clothes and using the grotty clothes to wipe down removes most of the sweat, then just use the old shower in a can to freshen up.
Marketing companies may have made you care, but as Garth Marenghi states 'if you use antipersperant to block pores the sweat will get out in other places, such as the face and neck, if you block all your pores with antipersperant, then you start to sweat inside and that gives you cancer.' as I have discovered shaving your armpit hair off simply allows your sweat to run all the way down into your underpants elastic band, so wipe up.
Furthermore I believe that attitudes would change with the forced behavioural change, people would simply adjust their attitudes to say 'formal clothing just cant happen in a world where everyone rides bikes' and three piece suits will be known for the massive impracticality they are.

Children, when small they fit in those dork seats, when larger they can ride themselves, elstwise stick them on a fuel-cell bus, or walking buss, or stick them in a group of kids on bikes to go to school like some kind of duckling, problem solved simple like.

People who live in the country, I imagine a plow on a tractor, a thresher, and maybe even helicopters to russle cattle could be construed as commercial vehicles, but people in the country live far away from everything. Maybe like city relatives some kind of break could be given to country dwellers over the car thing, but that would seem like a cop out, also the hilly terrain means would be great for producing world class cyclists. Instead you could get infrastructure solutions, like a general depot to do food drops, and build bike paths for the express purpose, with solar lights and weave through the country in ways far more economical than the country roads as they could cut neatly between paddocks without the disruptive effect a dairy tanker road would take.

The economy, without an overcomplexity of parts to break down, bikes have a tendancy to be around for 25 years if kept in good nick, and repaired rather than rebuilt. They are also divisible or easily made into a 1 bike to 1 person convenience, highly tradable and require very little maintenance compared to automobiles.
No petrol, but peoples appetites might increase with their metabolic rates as they adopt a less sedentary lifestyle.
So the agriculture industry might spike, whereas the petrolium industry would probably sag, furthermore you'd have manufacturing take a dive as the demand for automobiles was abolished and thus having tax subsidies for these industries would become a complete joke.
But you'd get some rebound in the growth of bike service shops and shit, and Australia would no doubt start having home grown bike companies spring up, mayhaps even producing competitors for the mighty shimano in parts. Although our manufacturing practices have never been world class, our R&D potential thanks to education is up there.
Furthermore, the reliance on mass transit for long distances would make the industry far more utilised and thus far more economical. Demand would spike, making people willing to supply mass transit on a larger scale, and cheaper eventually too.
The other benefit is that Australia would become a much larger country, you'd have more civic centers simply based on the fact that people are no longer willing to travel to the other side of town for entertainment. You could have multiple CBD's to cater for the spread of population, local community that shit.

What about the roads that are there? These would be awesome if dedicated to cyclists solely, when you think the average bike is what? genourously you'd put it as a quarter the width of a cyclist, so these wide spacious roads would provide the most luxurious bike paths in the world, traffic and congestion wouldn't be an issue for another ten thousand years. One could safely expand nature strips and put in more greenery with relative ease.
Furthermore, cyclists would pose no obstacle for Ambulances and police vehicles, both of which there would be a diminished need for in an absense of cars.

Now it would have to be enforced for one thing, as bike usage increases towards any utilisation of significance then the market for petrol is going to diminish and prices and margins probably would drop to make driving more attractive and thus cycling less attractive.
Higher petrol prices don't mean people are going to give up on cars alltogether, it may happen in Australia because Oz represents piss all of the world population, particularly as China's appetite increases, but that said market forces would probably find a new balance meaning a slight increase in commuter cycling.
100% utilisation is more of a big hairy audacious goal, designed as an exercise to stimulate my mind in thinking 'how could it work?'
One would expect a cycle country to work worst in a place with as small a population as Australia spread across such a land mass, but I am more convinced than ever that it could.

Furthermore exciting things are happening with bikes, such as the peddal powered washing machine, and bamboo bikes for developing nations in Africa. Then there's critical mass and the free bike repairs in exhibition gardens every sunday.
A world with only bikes would also yeild a hotter general population, and be much easier on a health care system. Obeseity which is linked to so many health problems I would expect to drop off the chart all together.
So get on a fucking bike they are fucking beautiful.