My wife and I just went to Florida in October for our honeymoon.
The keys and Disney are two totally different experiences. Disney is a great tourist spot, that is based on hustle bustle. The keys are laid back, do what you please and relax.
We did both ( Have been to disney 8 times, first time for the keys).
We absolutely loved the keys. We stayed on big pine key at the Barnacle B&B. We wanted to stay at Casa Grande but they were closed. Nice place on the beach.
I recommend going snorkeling and deep sea fishing. Bahia Honda state park is a nice park with good beaches with very few people. The only problem is the seaweed that washes up on the atlantic side of the shore there.
The swim with the Dolphins thing was kinda cool. I think that was on marathon.
I think my favourite part was the drive. Looking to one side and seeing the ocean, to the other the gulf, and miles of bridge ahead of you. Just an awesome feeling.