You are aware the distance from Tampa Bay to Key West is around 400 miles aren't you? (I live in the U.S. and have done this trip numerous times). Once your on Highway 1 at Homestead the drive becomes monotonous on the way down and interminable on the way back. While the quality of the roads is quite good, the traffic can back up unexpectedly and there's no where to turn off (You are in the middle of a sea). The speed limits are around 55 mph but the troopers patrol the highgway a lot and an accident, even a small one can back up traffice for miles.
You didn't say how far you want to go. You could just go to Key Largo (Of Humphrey Bogart fame) but if you want to do the whole length from Tampa, you're looking at a 6 to 7 hour drive.
I might suggest that, depending on how much time you want to spend, that you check into the really fast, modern and comfortable ferry boat that leaves Ft. Myers (and hour or so south of Tampa) about 8:00AM and arrives Key West about noon. If you didn't want to stay overnight you can return the same evening.
Check here:
http://ferryservicest...rrxuKcCFYjsKgodLxrBBQ
Even if you wanted to stay in Key West, it's a relative easy walk to most everything on the island...
Welcome to the U.S., by the way...