Baby Greys are just the cutest babies. It's been so long since my guy was so young, but he's been an amazing family member. He says the darnedest things, too, so get ready for that.
That's a great "baby cage" because young Greys are often so clumsy. I used to put a thick bath towel on the bottom of the cage and then put paper on top of that (yes, on top of the grate). They are so heavy and fall so hard they are prone to splitting their chest open. As others have said, it will make a great sleep cage when she moves to her permanent big-girl cage.
Looking forward to watching her grow up. Good luck with her!