When to move baby to the crib?

AW • Wife. Mom of 2 💗💙.
My baby will be 5 weeks tomorrow and my husband is adamant that we should move our daughter to her crib.  She is a noisy sleeper and since my husband is the only one working right now I am mostly getting up with her. However, I wind up walking back and forth from the nursery where I feed her to our bedroom and it makes for a long night. Also, I think he selfishly wants our alone time back and also she winds up waking him up all the time when he has to work an extremely long day. Part of me feels like it might be worth trying but the other part is worried! When did you all transition your babies to the crib?
Also I am open to hearing what worked for you moms and any advice you have for the transition!