Well, I know you have been exploring this for a while and it sounds like things are falling together and this would be a good move for your whole family. I tend to agree with what everyone else has said. Make sure the move is about you and work and what's best for the family and not about her gymnastics, that's just a bonus.
Also, if you are coming south instead of north of you (making an assumption here, sorry if I am off base) then I would recommend visiting several of the gyms down here that would be within commuting distance of your work and make sure you find the best fit. I know you liked a certain gym based on going to optional states and I can guess of one of a couple that that would be and they are great. But there are several north of the city that are very good and visiting a few different ones to make a good decision sounds like a sound idea as they all have different feels, coaching styles and philosophies. Also, the school districts/schools are of varying quality so I would keep an eye on that as well.
A competition is just a single glance into a gym. There are several gyms around here that have great optional gymnasts with compulsory programs that seem to be struggling a bit, so how does that effect the future optional program should your daughter get that far. There are also several programs that have smaller optional programs or teams but are building a great foundation for future success.
A competitive program is a full picture and so individualized to the gymnast and parents. It's not only about competition results but also training environment, philosophy, where the club has been and is going and what your daughter needs in a coach and how it all feels in your gut when you sit in the viewing area and how she feels when she is working there day in and day out. I know gymnasts and parents who are very happy at all these quality programs, big and small. It's all about finding the right fit for your daughter and yourself.
It sounds like you have the possibility of an exciting family adventure ahead. Good luck with your decision!