When you've been working in MA and you leave that job and file anywhere, even if you file the claim in FL, it will still be a MA claim, good for whatever your old state pays in unemployment benefits, etc. And in your case, this is a very good thing in regards to unemployment. While there is no "trailing spouse" allowance in MA, in other words, quitting your job to relocate with a non military spouse who has gotten another job isn't considered a valid reason to quit your job and get approval for unemployment, you'll still have a full set of base period wages in Massachusetts, which is one of the most generous weekly benefit amount states in the whole country.
What I would do, as soon as you get to Florida and have an address, file a claim for unemployment. This will be an "interstate" claim, will be based on your earnings from your job in MA, and will be quite a large chunk of change, compared to Florida's princely sum of $275 per week, max, IF you can get through their horrible and convoluted sign up system to get a claim set up and get through that terrible understaffed underperforming claims system.( Welcome to the southeastern third world part of the USA. I'm not real sure that giving up blizzards for their kind of state services is worth it.) But anyway.....
File the MA claim through the FL system, which they will know how to do, pulling in all the wages from the base period employer and connecting you with the MA interstate claims unit. This what you will have to do. You always file in the state you are going to live in. Eventually, they'll get you a claim set up and you'll have a decision made by MA interstate appeals about whether or not you can draw benefits. It will more than likely be a no, the trailing spouse thing. But that claim will stay in effect for one full year from the date of filing.
Now, quickly, get out and find yourself some temporary employment in your new home. Work enough to make 10x the amount of your weekly benefit amount on the MA claim. Then the job ends, or you are laid off (through no fault of your own.) You re open your unemployment claim and bingo, the disqualification is removed, and you have a nice claim set up to draw a maximum of 26 weeks during the original benefit year of MA weekly benefits. They may even have some school benefits available for you or way they can help you use your unemployment while attending retraining.
But file that claim, get it set up, and then begin picking up all the temporary work you possibly can. That will be the key, you've got to take something and work at it and make some weeks of wages and then be out of work through no fault of your own, and then the unemployment button is pushed on the MA claim.

