A Ford F-250 could be a whole lot of different trucks. 1970 model or 2016 model? 4wd, diesel, long bed, loaded with options or no options?
Is this 7,500 pounds what the trailer supposedly weighs dry or what you think it will weigh after you add all your gear and supplies?
I would say that is this is a typical loaded up 4wd crew cab diesel F-250 and the 7,500 is the dry trailer weight then you will quite likely run out of payload on the truck after you load the trailer and your large family.