Just a few issues to think about. For one, if you lift that early in the morning are you gonna lift on an empty stomach? Are you gonna be too tired to workout out?
Also, your classes are only like 50 minutes long. Lets assume that before you workout, you do some sort of warm up and then some stretching [hopefully you do this] and lets say that takes like 15 minutes. That gives you half an hour to do all your stuff. Lots of people would say that that is plenty of time for one body part, but its something you have to consider for yourself.
Also, your two classes are very close to each other. Under two hours from the end of one to the beginning of another. Lets say you eat after the first one to replenish your body. Do you get tired after you eat? Are you gonna be too tired going into your second workout??
Personally, if i had the time, i would break my workout up into two different parts during the day. But i would space the two workouts much farther apart otherwise, i would get burnt out. When i had time for a 2xday i did one at 9:30 and the other around 2:30. This worked well.
I think there are some things to think about, but there's nothing wrong with trying it and checking to see if you have the energy for it or not.
-Fatty