soulmama, little babies need comforting, soothing, warmth and feeding too often. She is not agitated with you - this is very normal. She's only a month old. Sleepless nights with the baby are famous for a reason. Things will get better with time. My five month old still wakes up often and I know this too shall pass away so I really do not mind. All he wants is a little love and I am in no hurry to have him become an independent sleeper. Forget about peaceful uninterrupted sleep for a bit else this journey will feel very long.
As far as a patter is concerned, just when you think your baby has a pattern , it may vanish the very next day. Be patient, take it as it comes and remember most new babies are like this.