First, how much exercise does he get? Do you have rules in the house or is he allowed to do as he pleases? Is your daughter firm with him, or is she excited around him? She can start by saying "NO" in a low voice and turning her backing ignoring him. Sometimes with children's voices the dog thinks they are engaging them in a game. He needs physical exercise as well as mental exercise w/ stuffed Kongs or basic training. You can attend puppy classes to tire him out as well as socialize.
He is old enough to be neutered, but, it does not guarantee the behaviour will go away. If your household is already strict and he has exercise and boundaries, and he's STILL acting out, then yes neuter. But if you haven't tried training then neutering won't make a difference. Address the home situation first, then make an appointment to neuter when your vet recommends.