Your ID is just used for identification purposes, not to verify your address, so your drivers license should be fine.
There are lots of forms of ID that work. Here is the Florida law:
Florida voters must provide current and valid photo identification at the polling place in order to vote. Acceptable forms of identification include the following:
-Florida identification card
-Florida driver's license
-United States passport
-Debit or credit card
-Military identification
-Student identification
-Retirement center identification
-Neighborhood association identification
-Public assistance identification
If the photo identification does not contain the voter's signature, an additional identification with the voter's signature is required.
For more information, visit the Florida Division of Elections site: http://election.dos.state.fl.us/voting/index.shtml