My son was in his cot in his own room at 4w 3d and he sleeps great, is only up once overnight for a feed and he is now 8 weeks. His room is just across the hall so i keep both bedroom doors open and baby monitor on x
Everyone does things a little different. My son has slept in his crib since about a week after he was home. He is almost 4 months old and pretty much sleeps through the night, if he does wake up and I am still really tired he will stay in my bed with me for a couple more hours. He does great and even though my house is small and his room is right next to mine, I still have a baby monitor. Puts my mind at ease a little more.
With my daughter, I had moved her to her room at 3 months. And it was great. My son is one month, and feel like I could already move him to his too. But will wait a little bit. And no, its not wrong to sleep with your kids. But know that it may cause attachment, and dependency when they need to sleep. My sister started taking naps with her kids in bed. And still (4yrs) has to lay with them to fall asleep, which is a drag. But its entirely your choice