Do not do it. Plain and simple. It will not work and it is not good for your baby.
Please do not add cereal. It will not change her behavior at all, if anything it will only cause digestive problems. Her tummy is too immature right now and she will not be able to digest it properly. My son was 9 lbs. 2 oz when he was born and could eat every 2 hours. It is completely normal for babies that age to eat that often. As they mature, the time in between their feedings will gradually increase. Just have some patience. Sleeping through the night is a sign of maturity, not of being full.
Just to comment speaking from experience- I never tried it at 1 month, but I did try it closer to 2 months- and the other posters are right- it doesn't change the behavior- my kids didn't sleep longer or anything, just gave them more gas and they ate just as often with or without the cereal.... DS did best on just breast milk then anything else- dd was very colicly (sp?) and NOTHING seemed to work with her, but I didn't bf her- eventually they will sleep longer...
I agree with the gals: No cereal, please...
Just feed her more frequently, she could be going through a growth spurt. Cereal in a bottle is a bad idea at any time (unless specifically instructed by your pediatrician). She is too little to digest it and it will not help. Frequent feedings are very common at her age- they need to eat on demand and some infants eat more often than others. It's hard when you are feeling pressure by family and friends, but don't give into it- you're the mom and you'll be thankful that you waited for the cereal (they suggest now to wait until 6 months or so) and just fed her more often.
Her digestive system cannot handle it and it can cause her to choke. Not to mention, increase her risk of SIDS. Don't do it. She will eat real food soon enough. Please do not feed her cereal until she is around 6 months of age.
Can't add much to what everyone else has said. Hungry babies need food. Not cereal, which is as nutritious as wallpaper paste.
Be sure she's actually hungry, and not crying for other reasons. If you are worried about how much/how often she is eating, check in with the pedi next time you go.
Congrats on your baby! I bet she's cute. Good luck, and remember, these early days pass quickly.
If she is finishing a full 4 oz bottle maybe she just needs more milk, try her with 5 oz bottles. If not then more frequent feedings will be necessary until she gets through this growth spurt.
Congrats on your baby.