Just like for getting married in the military, your basic pay does not increase by adding a dependent. If you’re already married and claim your spouse as a dependent, you won’t see your BAH increase either.
If your child is your first dependent, then your BAH may increase. Check the Official BAH Calc to see the difference between dependent BAH and single BAH. Usually a couple hundred dollars.
There may be some tax benefits as well, but you should probably consult a certified tax adviser for that information.