@L**
most places will let you apply for an extension when you have 30 days or less left on your current entry stamp BUT Jomtien sometimes says you need 15 days or less left on the stamp you're here on now.
There is no down side to going early because they ADD the 60 days to your current stamps expiration date (so you don't lose any days going early).
Take the original birth certificate, have your child's mother go (if she can) and take the child obviously.