It is currently being debated whether the sitter in this photo, commonly said to be a young Annie Jones, is in fact her.  There was a bearded girl who did go by the name Susan Ossiwosky (see HERE) but Annie was already being promoted with the stage name "Annie Jones"  as early as age 3½ in 1871.
www.quasi-modo.net
(right) Annie and her mother Margaret at the start of her career with Barnum's traveling show. ca 1873
Two pages from a 5¢ souvenir pamphlet "P.T. Barnum's Great Moral Exhibition", 1873.  Note Annie's name is not used here.
(left)1873 news ad for Barnum's show.  The "bearded girl" is mentioned under the "Talking Machine" heading