Thank you for your query
Firstly if your dog is immunized you don't need to take any vaccine
. Secondly Vaccine taken within 72 hours is good enough. Thirdly vaccine is to prevent rabies
and not treat infection due to the bite or pain. You will require analgesic
for that or if it is infected you will require dressings and antibiotics. Consult a pediatric surgeon and he/she should guide you. But you don't need to worry too much. As far as the more dreaded rabies part, you are safe.
Hope that helps
God bless you