Kite Republic are teaching through winter in St Kilda.
Give them a call and they sort you out for lessons if you want to start straight away, otherwise wait till September/October when its getting warmer and the wind gets more consistent again.
Not sure if I would buy a trainer kite as you can use the school trainer as much as you want after your first lesson. Rather spend the money on some decent gear once you finish your lessons.
Please don't learn with a person that is not a trained kiteboarding instructor! Go with a school and you'll be happier and safer.
You would not go bungy jumping with a random guy that has a rope, kiteboarding (although very safe when done right) is an extreme sport.
Btw, wind looks awesome for this weekend according to the forecast so far. Perfect time to get down to the beach