I know it's not much help but this does seem to be a common thing with a lot of babies at this age (certainly was the case with DS) and I think it is partly to do with them coming into light sleep, and partly to do with digestion/gut maturity which all just seems to get better with time. I'm not sure there's anything really that can 'fix' it as such as it sounds like you are getting on great during the daytime
Perhaps (if it's not a silly suggestion) you could try earplugs so that you won't be so disturbed by little noises, but can still hear a cry if she really needs you? Or could you head off into another room for part of the night and let your partner handle the early morning to give you a break? Hang in there, many of us here have found that this phase does pass eventually x