I agree that it's not clear why Clem is so much more mature than the adults who aren't able to cope with the environment like she does. However, she helps kill zombies and even the stranger, so it's clear she's not operating like a child. So it seems ok how she responded to Lee.
Clem rarely acts like a child. She doesn't get too frustrated and can see the bigger picture. She's usually reasonable, cooperative, and brave. She does get a bit excited and try to help Lee even though it puts her in danger, and she runs away because she doesn't want to give up on her parents. Apart from not having the judgment of an adult, she acts more mature than her age.
Clem is an unusual girl who can adapt to the TWD. Some kids are never really kids, and that's how Clem is.