It probably wouldn't hurt to start inquiring now since some (although not all) hospitals only take new grads at certain times during the year ... usually in December and May/June during graduation time. And, in a lot of cases, the hiring gets done as soon as three months before graduation.
Some hospitals like to group their new grads together so they can train them all at the same time and, if you happen to apply after that period, you may have to wait for the next round of new grad hiring if you want to work at a hospital that does this.
But, you're also in a different situation since you're applying from out of state. I'd call a bunch of hospitals and ask the recruiters how this would work with your particular situation.
The way it works in my area is that you have to get an interim permit from the board to work in a new grad program because, it can take several weeks to get your NCLEX results ... even if you take the test early. If you wait several weeks until
after you get your results, some of the new grad programs are either already filled or they're so far along with training their other new grads that they can't take anybody else until the next round of new grad hiring.