All that can presently (December 2022) be gleaned about Baby Abbot from sheet music covers and by Internet searching is that she was presumably an American actress/singer whohas been featured on just one work namely I'm Jealous of You (1905) words & music by Walter Coleman Parker, and published by Parker Music Co, New York, USA
Her portrait on the left is taken from the same work.
Surfers are welcome to contribute any further information about this performer.