The fitted will be wet all over. You will have leaks if you do not have enough absorbency or you have gaping around the diaper. I put my son in a sbish snapless with the small insert and wool longies. The sbish is always soaked and wool is damp but we don't have any leaks. If we did, I would add the second doubler.
If baby is still waking why don't you go ahead and change her?
Mama to Dillon '10 and Wyatt '12