no need to leave him or do anything really.
Just stop and think for a moment.
Yes, of course he can be your boyfriend for as long as you both like, just enjoy spending time together.
However, may living together and being partners....not so good.
Unless he changes/gets a job/or at least tries properly
So move into your new place ALONE. Tell him you are not breaking up, you very much love him, you want to stay in a relationship, but for the two of you to actually live together you need to be PARTNERS, not just boyfriend and girlfriends. And the partnership can only work with both of you pulling their weight.
In your shoes, I would disengage completely from his job search. I would not slave-drive, or nag or even enquire. I would completely ignore the issue once you have made it clear regarding your future set up.
That way it is completely up to him.
You are not his mother, so stop acting that way.
You are an independent woman, with her own plan. A nice guy that you love, who might even turn into a partner.
Personally, i do not believe in nagging, I think it leads to arguments, martyrdom and boringness.
Even in a partnership you can remain independent and strong and loving.
Just do your own think and let him simmer, I would not even ask how the job search is going, I would make my point, then disengage from his jobhunt, and quietly move on. Maybe he will follow, maybe not, but that should surely be up to him.