No, that is not normal and she needs a trip to the vet
. I have never, nor ever heard of a healthy dog of any breed just having pee come out while sleeping or resting. She isn't feeling the "need" or urgency, and therefore, there is a definite problem. She is way to young to accept this as a permanent problem. Please let us know what the vet says. I hope all goes well for little GiGi.