A.C.
Make sure she's not cold. That would wake her up every hour. The temperature drops between 2-6am, so make sure she's bundled up or get a space heater. Feeding the baby when she wakes up every hour would not help her metabolism. Her body needs a daytime schedule (3 1/2 - 4 hours apart) to learn when it's time to eat. Even if she wakes up at night, don't feed her. It will become a habit and won't end. At 4 months, she's capable of sleeping through the night. I would suggest reading babywise. I used the babywise book and both of my daughters slept through the night at 9-10 weeks. Maybe a combination of both books will help get your baby on track. Good luck!