My 3 month old puppy is very active during the evening/night, and also has trouble falling asleep. A few days ago I started taking him for long walks, three times before bedtime, then playing with him a bit right before going to bed, and it's helped a lot.
I'd suggest trying the same thing; do something that'll tire your puppy out right before bedtime, let them get out all that energy, and maybe it'll fall asleep without as much whining.
-Tim