Hello Jana,
I can see you feel strong enough to try to ski by yourself (no teacher) but you are just not sure. Don't be affraid - me and many my friends - we tried without teacher. There are some easy blue pists in Zürich area where you can practise, specially when weather conditions are good and there is not many peoples.
I am taking my friends - beginners - to Flumserberg on first Sunday of December (
www.flumserberg.ch). Let me know if you would like to join us(still 2 places in the car).
Tschüss!