There is no time as to when you should start hiring a mover. However, there are several factors to consider before hiring a mover and they are the distance covered and the stuff you will carry. The time of the year you want to move is also important. I would advise you start hiring now since you are moving in a month's time. Learn more from http://www.gentlegiant.com/moving-resources/plan-a-move.aspx.
I agree with Joke.Jeff there is no like limit when you should start hiring one. if you're still looking for a moving company I highly recommend High Touch Moving to you I've used these guys in the past and they were amazing. they also have free quotes online. http://www.hightouchmoving.com/long-distance-moving.php