How long will it take?
Young children learn quickly, however they are just as quick to foget! They need regular revision and practice (at least once a week) to retain skills and progress.
Of course babies are unique and will learn at their own individual pace. They all plateau (or even regress) occasionally. Continue with lessons and stay positive as your baby "cements together" new skills.
As your child grows, swimming skills will also develop and extend. There is no end-point to the process. You are embarking on a journey that begins with water confidence and will lead to a respect for water safety and a love of swimming that will remain for life!