Welcome aboard! The round trip is almost 400 nm so, even if you were to overnight it there and back, weather
willing, you wouldn't have much time to enjoy the keys. (If you don't overnight it, you won't make it there and back in a week). Bad weather
crops up, and you've got no extra days for a buffer.
There are lots of charters out of Miami
and a few others in the Keys...should be easy to find them on the internet
(I've never chartered, so I'll leave that for someone else).
Winter/spring is the big season due to all the "snowbirds," with later March and April providing the best weather during that period...but fall might actually be the best time if you're flexible, with weather as nice as in the spring. If you can stand the heat and bugs, summer might work too (I've never been there in the summer). Good luck, and happy cruising!