Don't "break" her of this!!!!
Having a sweet "lovey" like a blanket is one of the most precious childhood experiences....My 17 year old was a "blanket baby". He still is! It never got in the way (he didn't have to drag it to sleepovers or anything) but he still loves having a special blanket.
They have changed over the years from that beloved first one that got so tattered to one that we lost (an awful night), to various incarnations of fuzzy or pretend fur blankets.
My husband even sewed him a lime green fur on one side, black satin on the other side blanket for his 17th birthday (it was his dad who sewed the first blanket when he was a baby). He loved it more than the game system and stereo he received!
Just cover her with her precious lovey and tell her that it is the one closest to her skin and that you'll lay this other blanket on top to keep both her and her lovey warm. Always worked for me. By pretending the other blanket was cold, he would let me cover them both.
I wish I was still at that precious stage! My other boys had "lovies" (a stuffed kangaroo and a bear) who make their appreance from high on the closet shelf when they are sick or there is a trama (everyone slept with their lovies when the dog died).
Enjoy this precious precious time!