It wouldn't be possible for Nobita and Doraemon to breathe in outer space; also, unless they have artificial gravity in their spaceship, they would be floating in it.
Nobita or Doraemon and his human friends would be 6 times lighter walking on the moon than on Earth, and they would be bouncing and floating on the moon, which the movie doesn't show.
It's impossible for Doraemon, Nobita and his friends to survive on the moon without wearing spacesuits with oxygen tanks as there's no oxygen or plants on the moon and it gets very cold when there's no sunlight.
The beanie hats Doraemon and Nobita wear are too small to be practical to fly; the propellers on them need to be much bigger with enough power to lift the characters off the ground. Also, the hats need safety harnesses that wrap around their shoulders to prevent them from flying off their heads.
Doraemon the cat is seen flying into outer space with his human friends in a hot-air balloon; this wouldn't work as the balloon would pop and fall, and it's very impractical for flying in outer space. He would be better off with a spaceship or rocket.