Congratulations on your new horse! This forum is perfect for asking questions and finding information about anything horse related. There are so many helpful people on here, but just be prepared for complete honesty! :p
I agree with everyone on establishing trust with your horse. Before you start displaying your dominance though, I would spend some time getting used to your horse and letting him get used to you. Just watch him in the field, or put him in the arena and just sit back and watch him. Let him sniff you, lead him around for a while, pet him all over, and let him get used to you handling him.
When I got my current horse, I kind of rushed the "I'm your new owner, you are going to respect me now" thing. He was my first thoroughbred and the youngest horse I had ever bought, so I was a little nervous. If I had spent more time getting to know what kind of horse he was on the inside, I think I could have skipped over a few little issues we had. We came out best buds on the other side, so don't freak out if things get hairy at first! As an 18 year old QH, I don't expect you will run into many problems. Just always be patient with him and he will reward you for it.
I'm so happy for you and your little girl, I hope you guys have tons of fun together!