ouchie!
Lexi had a nail very very similar to that when i first got her, and when i took her to the vet for a checkup, he removed it and gave me some antibiotic ointment to put on it.
recently, another bad nail actually just cam out of her little toe socket, it was a really clean slide out and no infection thank goodness.
Can you take Rosie to the vet? Im wondering if that would be best in case it becomes infected or snagged on something... it LOOKS like you could almost remove it yourself, but thats a scary thought i know ... it looks like the nail could come off easily, but there is more "nail" or tissue of some sort growing behind it ... hmmmmm. poor Rosie. im wondering if its dead tissue and she cant feel it or does it seem to be bothering her. i know they mask pain TOO darn well.
I would take the vet route myself, just to be cautious and to get it removed safely.
I hope everything works out!!! Let me know how it goes!