We do most of our Gulf diving in the Panama City area, but I've been out in Gulf Shores 3 or 4 times too. With the exception of one trip there (that we would have been smart to cancel since everyone onboard got seasick and we ended up cancelling the second dive anyway) I've had better visibility in Gulf Shores than in Panama City. Close to 80 feet once, which is unusual in the Gulf. That time of the year seems to be when the big schools of baitfish come in, which are interesting to watch.
We've used Down Under Dive Shop every time. They now have a new Newton 46, which is much better than their old 6-pack boat. It's a professionally run group, and they are very thorough on dive briefings which would be nice for you so close after certification. They are on Hwy. 52, just over the bridge on the right as you head to the T.
Just remember that the conditions in the Gulf can vary greatly, and if you think it's too rough for your experience level, don't be afraid to cancel. I haven't been there post-Ivan, so I'm not sure if there are still visibility issues there. Even if you end up with limited visibility, there are usually lots of little things to look for too. We've done a couple of the Liberty Ships and a Navy Tug. There aren't any natural formations in the area, so you're limited to wrecks. I personally don't care to dive the jetties, but have heard of people that do. Haven't tried any shore dives there either, but you can ask and I think get a map to one that's easy to get to off of one of the local hotels (Holiday Inn?).
We're heading to Rosemary Beach this weekend and are going to dive in Destin.
Have Fun!