The Australian reports that further amendments include removing the need for trans people to have sex-change surgery before switching gender on official documents.
Premier Will Hodgman relies on the support of Speaker Sue Hickey, who votes as an independent.
"I do think the world is changing and we need to be open to considering things that might discriminate or harm somebody. I'm very open," she said.
Transgender activist Martine Delaney applauds the move, saying the removal of gender on birth certificates would have a benefit for transgender people who are applying for new jobs.
However, not everyone agrees. Feminist group Women Speak Tasmania believe no changes should be done to birth certificates.
The Australian Christian Lobby says the move would "homogenise humanity".
"If you are legally a transgender woman, even if you have a penis you can go wherever you want in terms of women's safe spaces," a spokesman said.
