But she said she was told by staff that her details didn't match, Fairfax reported.
"When they came to me they said 'your details don't match up'.
"They were just like, 'look, you've got five seconds to provide some ID, prove who you are or you're not getting on this flight'."
Miss Hume alleges she spoke to a manager who said her details didn't match up, saying 'your details don't match up, it says Miss Darci, you are clearly not a Miss, Sir'.
Miss Hume said she had "never felt so humiliated".
A Jetstar spokesman told Fairfax that Ms Hume's gender was not an issue when they asked for identification, and regretted any offence caused.
For travel within New Zealand, the airline requires that identification be shown if requested.
This could be a passport, driver's licence, birth certificate or citizenship document, student ID or a company-issued ID.