Never rented a bike myself, but there seems to be a few available with a quick Google of " rent BMW bike Australia" like http://www.compassexpeditions.com/re...cycle-rentals/
Don't know anything about them, just one that came up.
Big place down here as you might know, and "neat stuff" can be a damn long way in-between.
End of March it'll still probably be pretty warm, possibly a little wet or mixed weather, something to remember.
What sort or riding do you want to do, and what sort of stuff do you want to see?
Do you want, coastal, country, outback.... or a mix?
10 days could get you a fair way if you are into long distance riding... but if you want to wander round seeing the sights that'll limit your travel time a fair bit.
Sydney south to the Victorian border is say 9 hours or so...
Sydney north to the Queensland border is say... 9 hours or so...
Sydney west to the South Australia border is say... oh, 9 hours or so..
Sydney east to NZ is, well.... wet!
note: this is our state of NSW for example... http://www.visitnsw.com/things-to-do