Stroller Grandma is an extremely rare ghost in Project Zero III. Defeating her will get you the "Notched Arrow Key" which will lead to another ghost battle leaving you with a helpful Camera Function.
It is not known what Stoller Grandma was called when she was alive and the game doesn't tell us much about her. Her entry in the Ghost List says that after her Grandchild died, she grew distraught and dug up the baby's corpse, keeping it in her stroller.
As you can guess, Stroller Granma is old. You cannot see her face well due to her long grey care covering her face up. She pushes her stroller with her everywhere.
You hardly come across Stroller Grandma, she's extremely rare. In Hour IX, if you go to the Foyer (Where Rei started at the beginning of the game) you will get the opportunity to battle her for a key item. She'll come at you from the front, shuffling quickly with the aim to ram you with her pram. She'll attack you twice but then she will disappear. You can only get her when your Capture Circle is red an she won't move back when you take the shot. When you defeat her she'll drop the Notched Arrow Key which you can use on the door near the Manor's exit. This will lead you to another battle which will get you the "Measure" function for the Camera Obscura - it shows the HP of the nearest ghost.
If you avoid this area in Hour IX then it's very unlikely you'll come across her at all.