Tinkerbelle is a Chihuahua...she is 5 years old, but still needs to go out occasionally during the night. If she is really whining, I get her outside. Please leave water for the pup, chihuahua's have a tendancy to have episodes similar to low blood sugar and should have water and a few nibbles of kibble at all times...
Have you considered a peepee pad for overnight? We have one under our dining room table for emergency use during the winter and for overnights. Tink understands that it is not for regular use, and will let us know she needs out...but...if I'm not home and she can't wait....I would prefer the pad than anywhere else.