Honestly I believe you should do what you think would be best for you in life.
Just like most people, my life was not easy growing up, and the things I regret most are things such as not having been able to find a way to move out when it would have saved me from some of the worst blows I took. Blows that honestly I felt coming long before even fully realizing their extend. I was in a bad place even before then and if in all that time I had just managed to get one of my requests answered I think things would have turned out a lot less painful for me and I would have either dodged the blows or found an outlet.
You took the steps already to gain permission. You did so because simply you feel a need to. Trust that, it is your intuition, instinct and for all intends and purposes it might as well be precognition. As for breaking it to your dad, you could always just tell him the truth which is that you need this to get some of your thoughts and feelings sorted out and to do so you need a change of scenery for a while.
Whatever you decide, it will have its benefits and its setbacks, it won't be easy either way. But if your intuition/gut tells you to do something. Then I think it is wise to listen.