For our sons first visit at 6 months we got him the 1st visit button and Mickey ears with his name embroidered on them. When we went again when he was 15 months we got his first hair cut there. I waited until the last day of our trip to do it....thought it was going to be so sad but ended up being pretty cute! Michael completely covered him in stickers and talked very gently to him. Then he started cutting. My son sat there so good while he took one sticker off at a time and handed it to me and daddy. Michael saved every piece of hair and wrapped in up in a tissue with "pixie dust" (mickey head confetti) and sealed it with a Mickey sticker. He then got a certificate with his name, date and who cut his hair saying first hair cut and a pair of Mickey ears with "first hair cut" embroidered on the back. Can't remember how much it costs, around $12-14. You can't make a reservation, just stand there and wait. Tell them it's your baby's first hair cut and he/she will get the royal treatment!
We also went to one of the shops in Frontierland and were going to buy those small twirly lollipops. The woman told us that since we bought those and our son had never had a lollipop before that she'd give us a certificate for a "magical moment" that said first lollipop and that date, etc. I think they have all kinds of different certificates that you could get. Just ask a cm or someone else on here and I'm sure they'd fill you in. (actually I may post and ask myself! We'll be there again in Sept when our son will be 2 and his 3rd visit)
You can buy first visit t-shirts, 1st Mickey t-shirt, etc. They also have my first Disney bear and my first Mickey.