Yeah, loads of providers let you do that, depending on the type of connection you buy.
If you're in an NBN area, that's first choice. TPG / dodo were about the only one with unlimited downloads though - and they are the two bargain basement providers (but are mostly fine). iinet is better, and some of their plans have very high limts.
No NBN, then either ADSL or cable. Adsl needs a phobe line to be active so you'll probably have to keep paying at least that bit of it and just switch the dsl on and off.
Cable - you'll likely be contracted at least for the first period.
Practically speaking, a cheap naked adsl service (a phone line is there, but not usable for calls) can be had for a little over $50 a month - so my choice would be get one of those on permanent basis and just suck it up.