First, congratulations on your new baby!
I co-slept with both of mine - still do with 8 month old DD, so here's what I think.
The research on co-sleeping is really hard to interpret, because no-one seperates SAFE co-sleeping from accidental co-sleeping. Accidental co-sleeping is not very safe.
Crashing out together isn't ideal, especially with a load of pillows around.
Do you or your partner smoke? Drink? Use any recreational drugs? If yes to any, make the effort to get your DD into her own bed, because co-sleeping is not safe for you.
If no, try letting your DD doze off on you, then gently rolling her onto the bed next to you, well away from pillows, and in a space where the duvet can't get onto her - keep it tucked under you maybe? Does she have a gro-bag? They are great.
She may be OK close to you but not on top of you.
It can be (is!) a lovely way to sleep, but you need to make sure that your DD can't slip into pillows or duvet if she or you move.