these guys
http://www.rentabike.net.au/ apparently offer Gitane MTBs for hire, as well as
"touring bikes with panniers and lights if you want to head off overnight "Around the Bay" down the Great Ocean Road or beyond."
don't know much about them, just remembered seeing an ad in a tourist brochure somewhere. might be something to look into. i might stop by one day when i have more time, just to see what' they're all about.
also, even if it's a slim chance, consider packing your bike, if you don't mind subjecting it to airline baggage handling, it may be comparable in price depending on how long you'll need to hire the bike for. plus it'll be a guaranteed comfy ride.
Edit:
- for Melbourne, you're looking at the Dockland's store, if you were confused.
- You probably want to ring/email ahead about taking it to Tassie, see what they think about it.
Also,
http://www.bv.com.au/bikes-and-riding/10978/ has the above listed, as well as a link to shops which apparently do hire. Again, ring/email ahead and see if they don't mind you taking it over the Bass and out of state.