Here is a case where each dog is an individual and you need to know your own dog. Males as a rule mature more slowly, both physically and mentally. If your male still seems very puppyish and in that gangly adolescent phase of development, it might be wiser to wait a bit or run him only at trials where the course plan is short and simple with no sharp turns. When in doubt, ask the advice of your dog's breeder or other experienced Deerhounders. Otherwise, there is no reason you can't go ahead and run your Deerhound at a year of age.
Many Deerhounds successfully do so every year.
Don't let your dog wear herself out this way. Keep her out of sight and sound of the lure until it is her turn to run. At most, let her watch just the course preceding hers. And try to park far enough away from the course that your dog can't hear the lure machine or watch the courses in progress. You will want to purchase proper equipment for lure coursing.