Hi Lucy,
I started taking Kate to Stateswim ($11 a lesson) when she was 4 months old, she loved it and learned to take a breath before going under.
It was a really nice experience for both of us to get in the pool together and have fun with the other bubs and mums.
We stopped going when I broke my foot when she was about 10 months old and I didn't put her back in lessons 'til she was 2 and a half and she hated it then. #-o I wish I had kept it going right through.
I say give it a try and see how you and Olivia like it.