This is always a point of contention when somebody brings it up; but, the objectors always seem to object based on the IDEA of shooting bigger game with this little round, while guys WHO HAVE ACTUALLY TRIED IT seem to agree it works.
For my 2 cents...As long as you're competent with your rifle, the game won't likely be able to tell a 7.62x39 from a 30-30.
If you handload, I'd try heavier bullets if you're going for moose. .310 and .311 Bullets designed for 303 british will work perfectly, and quite a few guys have reported reloading regular .308 bullets in thier 7.62x39 rifles and getting good results.
I've got a batch of 165gr RN, loaded in 0.5gr increments, that I need to hit the range and try in my SKS. I have cycled them through my rifle and they (manually anyways) feed completely properly.
If you do get out hunting with your rifle, post some pics and some results. Results...the best way to sort out the age old - "Can I kill a moose with a 7.62x39" threads.