Another one who has taken baby swimming from 12w, and to classes that have always been full of wee ones after they've started their jabs. (Honestly quite surprised how many people on here are saying to wait!)
Put your swimming costume on at home.
Three towels, if you can - yours, one to wrap baby in when you get out the pool, and then another one to actually dry baby with. Or your dressing gown, you do freeze slowly while getting baby dry and dressed!
If your pool lets you take your buggy to the poolside, put at least one towel under baby as swim nappies don't actually hold pee (learnt that one from experience!)
Several swim nappies, just in case.
Be prepared for them to not seem to enjoy the experience the first time or two, and for a lot of screaming when you are getting them dressed.
And if you are bottle feeding, have a bottle or carton to hand as they're often starving straight afterwards.