Too soon to apply?

My boyfriend and I are likely moving to another state towards the end of Summer (probably late September). I will be looking for hospital jobs, maybe with some extra supervisory responsibility, like a clinical unit coordinator or something. Is early July too soon to apply? I would aim to be starting the first week of October at the latest.

I was going to wait until closer to August based on how quick the hiring process has been for previous new jobs. However, since leasing an apartment is sort of dependent on where we'll both be working, I'm hesitant to wait too long. I also have only a few good stretches off between now and September when I could travel for interviews and share time.