First thing - you have nothing to worry about, even if you don't get into the park until 9. The time on your reservation is not an absolute, especially around park opening time.
If you get in the gate at 9, and go straight to the restaurant without rushing, you'll be just fine. Even if you don't speak to the hostess until 9:18, there will not be a problem. They understand that things get a little chaotic around opening.
Second - there is an entry area devoted to those with early reservations. This area gets a big rush right at 8:00. Afterwards, it slows down a bit, and I believe it remains open with just a couple turnstiles. Since your seating time isn't until 9:15, I can't be sure if you'd be admitted before 9, but with a large party like yours, if the lane is still open, my guess is that you would.
Main thing - don't stress, and don't rush. If you get to the gate by 8:30, you should be able to get to the restaurant and enjoy your meal with no problem, whether you're admitted early or not.