Unless you are considering condos in the area, you can generally expect that both you and your pets will be welcomed. As a rule of thumb, one can normally rely on single family homes to allow pets while condos will vary greatly from one complex to another.
Pets are allowed at Stoneybrook in Sarasota. If you are renting, the individual owner who is renting the home has the right to say whether they allow pets or not. So, you would have to find a rental that does allow pets if you want to rent in that community.