He is absolutely not trying to dominate her. It's been scientifically proven that domestic dogs do not live in 'packs' or have a dominance hierarchy.
Never respond to anything the pup does with physical punishment or restraint. We don't need to behave like dogs to get them to understand us, they know we aren't dogs.
For a dog that does get excited by the 'squeal when nipped' method, withdrawal of attention usually works. Any tooth contact should immediately stops the game. Your dd should stand stock still, cross her arms and totally ignore him. If you are there and he's persistent, you could reinforce it by quickly popping him behind a dog-gate or something. He should soon cotton on that it's more fun to play nicely and be allowed to continue the game. When he's calm and stops nipping she can give him a suitable toy and tell him he's a good lad for biting on that instead of her.
I also agree it's a good idea to get her involved in his care and training a little, closely supervised of course, as it all helps to build a good bond. If she can come to puppy classes with you and learn how to handle him appropriately that would be great too.
My pup is now 11 months old (and huge) and despite being a typically calm breed, has always been more excitable around my dcs, partly because they play with him a lot and he loves being with them. He wasn't massively nippy as a tiny pup, but like most puppies, he had his moments. Now he's careful to be gentle with all three dcs (12, 10 and 5) and knows he has to control his loopier instincts when he's around them. All three dcs can play tuggy games with him and get him to let go with a quietly spoken 'give' command/cue.
When he was very young I clicker trained him myself first to teach him the basic sit, down and wait and then taught the dcs how to use those learned skills to ensure he played calmly eg he brings them a toy and gives it to them, then he has to sit and wait until they throw it. They also use them when going through doorways and opening the back door to the garden for him. All this helps him to learn impulse control and to realise that he can't just be a bull in a china shop/hooligan around them and the rules are always the same, regardless of who he's interacting with.
It's very early days. Training classes will help, especially if your dd can be involved.