Can airplane cabin pressure harm my baby?

No: The pressure in an airline cabin is normalized and if you are safe, baby is safe.

No...but: The changes in cabin pressure as the plane rises and falls can make a child miserable. You and I have learned how to equalize the pressure in our middle ear as the pressure increases or decreases. This is impossible to explain to a child. I found that having full "sippy" cups at take off and landing, and making the child drink from them, decreased the pain for both child and parents. Good luck.