We were in my grandparents pool from a couple of weeks old onward, and I had kiddo in the pool (a different one) from a couple of months old. I was actually swimming several months before I took my first steps (not underwater... my mum didn't believe in using the morrow reflex to teach infants to swim underwater. Not that she didn't believe in the reflex, she just thought it was too risky).
A number of safety things have to happen. Like watching for hypothermia (babies don't shiver, they have "brown fat" -aka vascularized- to keep them warm until the can shiver, so you have to watch for subtler signs). And you ALWAYS have to have 2 hands on them (don't use floaties at this age). And you need to go in slowly, so you don't shock them. AND not stay in for too long (as in try for 5 or 10 minutes tops, unless the pool is heated). But unless she's allergic to chlorine, or the pool is icy, you should be fine.