Welcome! I used to commute to/from the 125th St. station on the 1 line at Broadway, but I can't comment specifically on the A/C stop, which is over on St. Nicholas and where you will presumably be going to from JFK. In general, I will say that the neighborhood is up and coming, but since you are coming in late at night and are not from NYC, you and your daughter might be more comfortable getting off at a different stop.

A mile sounds longer than it should be, though - 5 blocks is only 1/4 mile, so you must be going crosstown, too? If you let us know what avenue your hotel is on, we can probably provide some alternative directions.