Newborn babies can't swim – they have to learn, just like they learn to walk. But most babies do enjoy being in the water and their reflexes mean they will be able to do primitive swimming strokes. You don't have to wait until your baby is immunized to take them swimming.
Babies can go into the water from birth. However, they can't regulate their temperature like adults, so it's very important to make sure they don't get too cold. Babies can also pick up an infection from the water.
Therefore, it's generally best to wait until your baby is around 2 months old before you take them swimming. Baby swimming lessons usually start at around 6 months.
If your baby is younger than 6 months, make sure the pool is heated to about 32° C. A large public pool would be too cold for a baby under 6 months.