I don't think ICG are into delving onto British criminal records to try to identify who "Jane" might be. It is ambiguous whether "Jane" is the convict (female convicts were rare, but not unheard of) or the sister (?) of the convict, to whom the token is addressed. WIth no date or name other than "Jane", I doubt anything defininte is going to come up in terms of a specific convict.
It's my understanding that there were people on the docks where the convict ships were leaving, who would make these mementos for departing convicts (for a fee, of course). Apart from the "Jane Brother" inscription, the messages on this piece are generic (so would have been supplied by the token-maker, rather than the convict themselves). It's likely that the token-maker had this piece ready made up, with just a blank space ready for the adding of the name. "Jane Brother" would have been meaningful to the person or people who requested it be made, but without that personal context, I'm afraid the meaning will have been lost.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis