Im a bad reader!
If you have a flock this broody belongs to then nix the cage, she's got it covered lol!
You could set up a cage with chick sized entries/exits so they can hide while mom does her chicken things.
They may never use it but the option is nice.:)
Give the egg at least 1 more day, they hatch staggered pretty often and no worries she'll leave if it is a dud.
The cage sounds nice, make sure it is secure and out of the direct sun.
As soon as mom looks ready, id go for it.:)