ktmNP, I would say for one bedroom it would cost you like 1500 - 1800 from Dallas to Florida. but also depending on which level your apartment is and steps they have to climb when getting the stuffs as well when dropping it off. You can also call several movers and ask for the quote. Make sure you tell them that whatever would be the quote that would be the final price. But make clear about the steps.

Don't you save money if you move yourself? You can rent a truck from Uhaul, Penske, budget etc. Btw, I'm a Uhaul dealer.