I am on the Atlantic side of Florida with a 1y old right now, he is having a blast! He is the same age as your DD, I have two older girls and we have been spending the last 10 days on the beach and that is about it. He still refuses to walk but he loves crawling through the waves, knocking down sand castles. We take long walks on the beach with him on our backs every night. Our condo walks right out to the beach so I go in and out with him multiple times a day. We eat breakfast, the girls and DH head out, I gather things up and then DS and I go out. When he starts to get grumpy a couple hours later, he and I come back in, I lay him down for a nap and then we do the same thing again when he wakes up. This honestly has been the best, most low key vacation I have ever taken with kiddos, no trying to get to point A and B before a toddler melts down, I just walk back inside when he is done.

I really, really, really wanted to go to Hawaii as well but DH wanted nothing to do with the time difference and 3 children so we came here instead. It is a 2 hour time difference and was rough enough for the first couple days, traveling threw DS all off and he was refusing to go sleep before 1am and then sleeping into 10am, at least we had no place to go!
My requirement was it had to be within an hour of Orlando because I do have a grandmother here and I wanted to be able to see her a couple times, and because I didn't want to do another plane change or longer trip. I settled on Cocoa Beach just because it was larger and had more things for Dh to do, he gets bored easier then my 3y.

Which we actually haven't needed because he has been happy as a clam not going out except at night for a fish dinner. I prefer New Smyrna beach myself, it is where I always went as a kid, but there are tons of towns/islands all over this side of Florida that is oil free so far.
anyway, happy vacation planning!