All that can presently (March 2021) be gleaned about Miss Nellie Moon from sheet music covers and by Internet searching is that she has been featured on 3 works published between 1870 and 1881.
The British Library holds a playbill from the Surrey Theatre, Lambeth production "Aladdin and the Wonderful Lamp" (c. 1880) from which her sketch is taken. She was billed playing the leading part of Princess Badroulbabour along with James Fawn who played Widow Mustapha..
Surfers are welcome to contribute any further information about this performer.

This list is derived from information provided by Monologues.co.uk which went down sometime in 2023.
The loss of this valuable resource is very sad and a mystery.