I highly recommend The No Cry Sleep Solution for any/all infant & toddler sleep issues. Another good resource is The Happiest Baby on the Block (video). You should be able to get either of these from your library. Both of these helped boost my confidence with a very difficult & demanding first child.
My son is very sensitive to his environment and the recommendations in this book gave me hope without feeling like we had to simply endure it. I do not agree with the cry-it-out solution. It tears you up inside and teaches your daughter that she cannot rely on people in her world. Also, if there are any set backs (and there will be), you have to resort back to the cry-it-out method each time.
Take your time & be patient. Don't rush her. Depending on her temperment, she may not yet be ready for this move. But don't beat yourself up over it either. You're doing the right thing by asking for ideas from others & keeping your mind open to options. What works for one may not work for another. But by trying different things, you'll find just that right thing for her.
For my children, they had to be tightly swaddled in the beginning. If not, they would wake within minutes of being laid down. Learn how to do it correctly. If she comes out of it (before the age of 3 months), chances are it wasn't done correctly.
Also, one of the best things I learned is that there is a "magical" time during which you should lay a child down. Make sure she's sleepy & dozing off but not yet asleep. If you lay her down at this time, she'll have a better chance at putting her self to sleep. Although, at one month old, you may want to savor these precious moments holding her :)
If she happens to fall asleep in your arms (or in the swing, or carseat), you should then plan to wait approx 15 minutes to move her. By that time, she should be in a deep sleep (floppy arms, very quiet breathing) and you have a better chance of easily moving her to another location and her sleeping through it.
Regardless of what information/tips you use, it will get better! :)
Keep us posted,
P.