E.,
My daughter just turned 1 today (my, how time flies!). She has been sleeping with a small stuffed lamb since she was about 5 months old. Like I said, it's small, only about 6 inches tall, so it's not something she's likely to get her nose buried in. She must really like it because when I've checked in on her the past two nights, she's been hugging it while sleeping!
As for blankets...I've been covering her lower half with a thin, receiving blanket for a long time. I have sort of stopped doing it, though because she wiggles around so much at night now that she doesn't stay covered anyway. But until they start moving around, they are not likely to get tangled up in it anyway.
Hope this helps. If you're uncomfortable covering your baby with a blanket, there are sleeps "sacks" you can buy. I'm not sure exactly what they are called, but they are esstentially a bag that you put them in (they don't cover anything above the shoulders, of course.) These work great!