Hey Bec, welcome to the forum! I'm in Canberra too & have been scooting for just over 6 mths now. Did the pre-learner course with Stay Upright - extremely useful, though a little too focussed on geared bikes. Have subsequently done a one hour private lesson & the excellent Scooter Skills course, but all of that is probably a ways off for you yet.
Both of the local scooter shops are listed on scooter sales (Moto Central and Motorini). Both are open weekdays and Saturdays til mid afternoon. Some of the bike shops also sell scoots, but don't know what their after sales service would be like. CMC have Yamaha & Honda, Joe's also do Yamaha, though both of these brands are probably out of your price range. These dealers often have second-hand scoots.
Having been riding for a while, I would aim for minimum 125cc, given a lot of roads are 70-80kph, which you don't realise until you're riding around all the time. Someone else here at the forums complained that he'd bought a 100cc & within a few weeks had found it inadequate for getting around town. You will be less limited if you get something 125cc or above (though I know a gal at work with a 100cc Aerox & hers gets her around in 80-90 zones no problem, as I imagine something like a Bee Wee would too).
Good luck with your licence and scoot shopping & hope to see you on two wheels soon. PP
Proud owner of a beautiful blue Derbi Rambla, still not sold on a name... Need suggestions!