I don't believe in using those electronic bark collars. Yes, it is uncomfortable for the dog because they receive a mild electric shock. You also have to be in a position to push the button on the remote and the dog has to be within a certain distance for it to work. I find the electronic shock to be a cruel and negative way to train a dog.
Jmcgee, shygrneyz has given you some good advice. In all likelihood, your dog is hearing something outside and she is just doing what comes naturally to her. Dogs bark to warn their pack leader & other members (you) that an intruder has wandered into your territory. They are also warning the intruder that the territory is claimed by others and he better stay away. Your dog might be hearing a car driving by, another animal wandering around, the wind blowing,. To a dog, noise means "intruder."
What have you done when the dog barks during the night? If you get up and pet her, walk her, give her a treat, or give her any attention, you are reinforcing the behavior. If you aren't worried about intruders during the night, I would suggest moving her crate into your bedroom or another room and yes, lock her in for the night. Ignore the barking. It might take a couple of weeks, but eventually, if you don't react, she will quiet down. Keep her crated at night for the next few months. When your puppy matures into an adult, you can start leaving the door to the crate open for her at night and test her again, if you want to. If when you do this, the barking doesn't stop or escalates, there are no-bark citronella collars that you can pick up at most pet stores. When the dog barks, it triggers the citronella spray. It doesn't physically hurt the dog. Here are a couple of links so you can read up about the effectiveness of the collar, how it works, and what it looks like:
Citronella Collars
Citronella Anti Bark and Remote Dog Training Collars