I remember when my 27 year old played at night! His father suggested putting paper on the floor. My baby would play with it, tearing it, throwing it and using it interactively with his toys. We'd play in the living room; and I'd lay on the sofa until he fell a sleep.
Since then, I learned techniques which may have served me better.
I've taught future early childhood teachers. If my memory is correct, your baby is addressing a developmental stage related to exploration and understanding the properties of objects. She is making sense out of objects by manipulating them and determining their strengths and vulnerabilities.
An adult example related to learning properties! When you buy a dress or pants, you try it on to determine if it fits. You also examine seams to assure it was sewed well and they will not separate as your body moves in the garment. You read instructions on washing/cleaning to determine the strength of the material and whether it will fade, shrink, etc. when washed or cleaned. The properties are 1) How well the item was sewn and 2) the strength of the material.
Your baby is learning traits of the objects in which she plays and the variabiities of their use. If she is playing with a doll, she is probably pretenting it is a human baby. She may hold it, nurse it, fuss at it by saying no, or even hitting it and attempt to disassemble it.
P.S. This is, also, an opportunity for you to determine "how" she is interpreting your parenting styles as well as her needs.
L., this is difficult for you. You are not resting. Try playing with her by making up games such as house where you manipulate objects, ie. clay, sand, paper!
When she falls asleep, sleep with her.
K.