You'll have to adjust the hitch on your Dad's truck to fit your trailer. So when you come back home, you'll have practice for that new truck!
Go for it! Use Dad's, then get a new one! Or, just get a new one now and save a step! Sounds like you've pretty much fixed in your mind you're getting one some day anyway. Might as well be today!
(By the way, that is really nice of your dad to do this. All jokes aside, you should take him up on his offer. He'll feel better and it will give him a sense that he's helping you out on something. Parents, of all ages, need to feel their kids ... of all ages ... still need them.)