Question:
Is there any problem for a baby to look at their reflection in the mirror?
Answer:
There are some people that have such a minhag. If it your minhag you should stick to it, but if it isn’t your minhag you don’t have to worry about it.
Sources:
Be’er Moshe 8-36 (1), introduction to Hatinok V’hiulohosov question 19 in the name of Horav C. Kanievsky shlit”a