Virgin are great with bikes, you won't have a problem. They sell really big bike boxes at the terminal, $14 in 2006. If you box the bike in Hobart you might be able to find one for free at a bike shop (with packing materials inside if you're lucky) but that means you need to (a) find one and (b) fit everything in the smaller box and (c) either be 1st on the airport shuttle, or get a station wagon or maxi taxi.
The shuttle might also take an unboxed bike if you call ahead and let them know.
There's plenty of posts on gear and cooking and camping techniques here, but most have a US focus. Have you got most of the stuff you need? If you're doing this for the 1st time another good site is
www.bushwalking.org.au/FAQ which has lots of opinions on equipment and techniques. It has some good commentaries on going lightweight which will be very, very useful in Tassie especially as you need to consider the weather.
You won't need to carry a stove or cooking gear if you don't want to, but I like to at least be able to make a cup of tea or noodles if it is cold. There are plenty of towns along your route but in the 1st few days in the hills and from Launceston to the east coast you might not be in one with an open shop or pub at night. Depends how the timing works out.