Hiyah,
I took DS to swimming lessons when he was 6 months. Used little swimmers in this size and DS isn't very big, but then he always had chunky thighs!!!
A few tips that might help:
Make sure you wear your cossie to the pool (I mean underneath your clothes!!) as it makes things quicker when you get there.
I took two towels and wrapped DS in his as soon as we got out of the pool. You'll have to drip dry for awhile whilst you see to DD but, wrap your towel round your head or you'll drip all over DD whilst your dressing her!
Make sure you take clothing that's easy to get on and off, for both of you, track suit bottoms etc. as you may find that you don't manage to dry yourself properly and trying to get jeans on when you're damp is a nightmare.
Have nappy sacks in a handy place for the nappy you take off before the swim, and the swim nappy.
If it's cool where you are, make sure you take an extra layer of clothing for DD and hat and socks.
Some classes provide changing mats, find out if they do and if not, then take a fold up mat or extra towel to put DD on.
At the class I went to we just moved the babies around in the water for the first lesson and moved in a circle singing songs. We used a different technique to Soupdragon's class, ( "1,2,3 mmmmm" then duck them under ) but I think they all do the ducking if you're happy with it.
As SD says, relaxation is the key. My DS absolutely loved it and was a complete natural in the water... unfortunately I had to go back to work so I couldn't keep it up, but I enjoyed it immensely.
Have fun!!
BR