Hi there.. this is so common around the fourth week. I know many parents of month old babies, who are finding it hard (hard is putting it nicely!) to help their little ones fall asleep.
Right now, just work on separating eating from sleeping. Keep awake times short.. so generally, a feed, diaper change and swaddle up for sleep is probably the best approach. As soon as you see the first yawn, then start your settling routine.
Have you checked out the announcement/sticky at the top for newborns/young infants and sleep?
Also, with newborn/young infants sleep, the first 20 mins. are light, with brief awakenings at the 10 min and 20 min mark, and then into a deep sleep after 20 min, and then wakening at the 40 min. mark. You mentioned that she wakes up after being rocked and then laid down.
Crying it out at this age is cruel, but I know when you're feeling frustrated and at the end of your rope.. you don't know which way to turn. I've been there.. Brendan was a very spirited baby, and had a rough time falling asleep when he was a month old. And I was at the end of my rope many times..
Another thing to look at.. using a soother. Newborns don't have the ability to self soothe, and sucking can be soothing. It can also save you from being a human pacifier!
I'll check back, or pm me if you need support. Hang in there..