I would suggest at least a few of your longer runs be at night, around the same time as the race will be. Most of the time, the reason for the early morning start times is a combination of it being cooler in the morning, plus there is (usually) less traffic to have to reroute for a half marathon route than during a race that occurs closer to mid-day.
Other than that, you shouldn't have too many problems, unless you happen to be a morning person. If that is the case, or you are an early sleeper, then I would recommend a nap midafternoon or so, then when you get up do your normal prerace routine, including the normal food that you eat before an early morning long run, etc.
Another thing is to check the race rules. If it is a night run, they may be requiring headlamps, tail lights and possibly running vests. If that is the case, I would recommend the Petzl line of head lamps, at least 30 lumens, and I really like the minimalist Nathan running vests. Get them early, as local stores may run out close to the race time (If the race is local) and get some runs in using them, so you know what the lighting is like and what the vest and light headband feel like.