Yes, there is quite a lot of choice, although it's usually for babies, children and families. To take one of the best examples, my baby radio is a mix of songs and nursery rhymes suitable for very young babies, children's entertainment and shows aimed more at parents - advice from childcare experts, parents' discussions and so on.

If you put 'online radio for babies' and explore some of the links you find that way, you will also find radio shows aimed just at very small children - for example, giggle which is aimed just at pre-school children. You can find similar shows in different languages. You have to search carefully though, because quite often the term 'baby radio' is also used to apply to programmes for new parents looking for advice.
You could also explore the BBC options - they have some material for children under 3, which might be nice for a baby too.