OK, I'll reply to this in stages.
A. The full car licence will make a difference, however, if you've got minimal time left on your P's, then if you get a motorbike licence before your P's expire, you will receive a Probationary Motorbike licence that becomes a Full Motorbike licence at the same time your car licence becomes a full licence, please see this link:
B. For a list of the accredited motorbike licence assessors and providers, please see this link:
VicRoads Link Check the list and find the one that's closest to you :)
C. I strongly recommend you get your bike licence and start test riding the various scoots on the market. What suits me won't necessarily suit everyone as it's very individual. That said, if you're looking at the Vino, scoots with similar sorts of styling are Aprilia Mojito, VMoto Montego, the Vespa's, the Bolwell Mio 100 (smaller capacity at 100cc) and probably a couple of others.
D. I don't know much about the Vino but the one I've taken for a test ride seemed to be put together quite well and was more than up to the task. The main reason I didn't go for it was the retro style isn't really my cup of tea.
E. The $4-5k bracket gives you heaps of choice, so shop around, find the scooter you like the most and get it. I spent $4k on my Benelli Velvet 150 secondhand, partly the styling (Italians seem to have a flair for style!), partly the fact that it runs a liquid cooled Yamaha motor in it, and partly the sheer amount of storage in it.
The above are my thoughts, comments and opinions only. Best of luck with your scooter shopping, hope to see you on the roads soon :)