gDiapers?

My daughter is 3 months. She started sleeping through the night (yay!) but she sets through her diaper and wakes up each morning with damp clothes and sheets. I've tried huggies, pampers, luvs, and honest company diapers and none of them keep her dry. I know I could wake up and change her but when I tried that, she woke right up and didnt want to sleep for the rest of the night. I tried going up one size thinking they might absorb more, but that didn't really work either. I'm thinking of putting a cloth diaper cover, like the gDiaper, over her normal diaper to keep her more dry but I'm not sure how that would work out. Any suggestions would be greatly appreciated!