I am familiar enough with the use of Jinx as a woman's nickname that it doesn't seem odd to me. I think it actually wasn't that uncommon among the World War II generation. However, I do think this works better as a nickname than as something you actually put on the birth certificate. I would put a name like
Virginia,
Gina,
Jeanette,
Jennifer, etc. on the birth certificate and call her Jinx as a nickname. Then she can decide when she's older if she wants to continue being called Jinx or wants to use a more formal name.