I'm always wary pf threads like this, because usually if you have to ask, the answer is no. But you're asking sensible questions, so all's good!
You seem super mature about this and you appear to have already talked it out pretty well with your lady. I like the fact you say 'live together' at weekends, rather than stop over. It seems more.... long term and as if it will work.
At the end of the day, you're 25, and big enough to make your own choices. If it seems right, go for it. If it's not working after a while, you can go home: it's not like you'd be giving up your own place, so if there were any issues, you'll still have a safety net.
And yeah, whilst you'll save more living with your dad, you'll have shit all clue what to do with it once you do leave! It's pretty daunting getting all the life responsibilities, so the fact you can do that by moving in with someone in an established household re: bills, rent, utilities is great.
i know for a fact if I hadn't done that, and had tried to go it alone, I'd have falled flat on my arse!
Again with the ''you're 25''- you aren't going to live with your parents forever. If it makes them feel better, once you've got your shit together, set up a savings account with a standing order for a little bit that you can spare each week. You end up with a hefty rainy day/mortgage fund without even thinking about it. I did it off a students income, and used it to get my house now c: But yeah, you aren't gonna be a million miles away, same person, maturity, yadda yadda. You're a grown up :P
As everyone else has said, if it feels right to you both, that's the main thing.
I agreed to live with my partner 5 months before we entered into a relationship, and so moved in one week after we started dating.... Even the craziest things can work, because we're still in honeymoon mode a year and a half down the line.
I wish you the best of luck hon :)