Sheherazade,

I definitely agree with LLB & Geonz - don't concentrate on your average speed at all - it can vary so much from ride to ride, depending on conditions - traffic, wind, terrain.
Just enjoy your time in the saddle - there'll be plenty time in the future (if you choose) to think about average speed, cadence, form, etc. etc.
Whilst these things are important - so is finding your feet (pedals?!) and just riding your bike because you enjoy it. Ride because you want to ride, you'll soon be eating up those miles and you'll almost certainly find that as your cycling muscles start to develop, so will you average speed.
If you do a keyword search on hills, you'll find lots of advice for improving technique, shifting, cadence, etc within this board. I NEVER look at my clock when I'm climbing a hill - why would you want to do THAT?!! I know I'm going slow, don't need a damn computer to tell me that!