Oh yeah-- she'll definitely "sink" into the mattress more than at home, since it's air. Unless you have a different kind. I might put her on her own mat beside your bed, that isn't made of air. There is a slight risk, I think, of suffocation due to face being pressed into the softness of the air mattress, and if both parents sleep deeply you wouldn't catch it. DS and I didn't have an issue because I was the only parent. He didn't "sink" because it was just the two of us and I put him on his own "side" of the mattress, rather than in the middle between two adults.
Hey, that poem is the one that Willy Wonka quotes in the Chocolate Factory!
Do you know of a milagro for selling one's house?