I need a little advice.

My baby is almost a week old and isn't sleeping by herself yet. She's been feeding and falling asleep on my chest as I sleep in the recliner. We try to put her in the bsssinet and immediately she starts screaming. She's also prefers to be on her side since she's able to do that already. Is it normal for her to not be in the bassinet at this age? I'm worried I'm spoiling her.