pack n play sleeping arrangements .. is this ok? how do you put your lo to bed?

My baby girl is only 7 1/2 weeks old and already outgrew her bassinet. She's only been able to sleep in bed with me for over a week now; she will not sleep longer than 20 minutes in her bassinet. I'm trying to break the cosleeping before it becomes too much of an attachment so I built her pack n play. My SO Is in the navy and is coming home for leave for a week before his year long deployment and my bed is only a twin. He'll be sleeping with me while he's home so I don't want her to get too attached to the bed and be up all night In her pack n play. Well turns out its my pillow that she really loves and needs to be sleeping on. The pillow is super thin and flat from being used so much. I know it's a hazard to have a pillow but this is the only way she will sleep and is what she would sleep on in my bed with me and I never had a problem. She would sleep next to me on the pillow with a blanket. The mattress part is also hard.. not too comfy! Being our first time using the pack n play I'm getting anxious.. but she's actually sleeping in it nicely.. I'm sleeping in my bed right beside her in case.. (the iPod is playing white noise for her until she's fully asleep). I'm going to try her crib out soon.. it's on the other side of the room so I'm afraid I won't wake up to her waking up or crying since I'm use to her being beside me.. so I'm waiting it out for now. How do you put your babies to sleep in their bassinet/crib? Pictures help! Thanks
UPDATE: I did take out the blanket and pillow after posting this!! I just want to see if this is ok for future references in case she doesn't sleep! I'm a ftm; my nephew sleeps in a pack n okay with a blanket but he's 1 1/2
Also, my heat in my house hasn't been working right so my room is often chilly. I know she's not too hot considering she shivers.
This is her currently: 
It took a while for her to stay asleep and to meal the pillow out from under her.. she's now waking up and fussing without it
 UPDATE: I tucked my pillow case on the mattress and watched her just to test out of its my smell she's clinging to like you ladies said.. she is fussing a lot in her sleep here and there.. but eventually she's actually asleep longer than 15 minutes without fussing! Maybe that is it. I'll have to sleep with her sheets for a bit