With support from management, it's taken off and she's got 27 students, some of whom are staff at the university, in her class also learning space tourism and advising corporations around breaches of satellites.
"Space law as a subject is starting to take off in the United Kingdom but there's still only one institution there that offers it as a subject."
As for how she came up with the idea, she said she'd been fascinated with space since looking up at the stars with her parents as kid.
"It's always been a niche area that I have been very interested in. I think it's just since I was a child looking up at the stars, and seeing comets and planets being pointed out to me by my parents ... [I'm] very into sci-fi movies."
She worked covering international law, war crimes and genocide before finally getting to get into space law.
New Zealand had a "burgeoning" space industry scene, thanks to Kiwi company Rocket Lab.
"As a result I set up an establishment paper which I thought would be quite useful because New Zealand has recently passed new legislation and establishment of a new safe responsible secure space industry, so ultimately the paper aims to provide students with an understanding of some of the key space law issues that are currently confronting New Zealand."
The law, the Outer Space and High Altitude Activities Act 2017, covered issues including granting permission to Rocket Lab to launch three sites for its commercial rockets.
"Rocket Lab is very much of the view that New Zealand potentially in the future will be launching more commercial rockets into outer space than the US," she said.
It meant there was "huge potential" for New Zealand to develop a sophisticated, technology-driven space industry.
While Russia, United States and China were the bigger players, India was also taking off while Australia also had a space programme.
"New Zealand is fast catching up. The aim of the paper is how to practice in the area of space law so they can advise both states and corporations regarding space law issues, including if a contract of a satellite is breached, what should happen?"
Although space was governed by the international 1967 Outer Space Treaty, which only allows for the use of the Moon and other celestial bodies for peaceful purposes, there were still a plethora of issues that still needed to be ironed out.
A crucial one was clarification over where national space ended and where outer space began.
"There's no agreement amongst any lawyers about where outer space begins at all."
Another topic was US President Donald Trump's proposed extra-terrestrial "space force", an idea Dr Brennan believed was "redundant" given the treaty's peace focus.
"Technically it's prohibited because the fundamental principle of space law is that any activity is supposed to be for peaceful activity so if you're putting together a space force well, you only have one thing in mind."
She said the cost was also out-of-this-world - up to trillions of dollars.
"He may not have foreseen this very well because any mission into outer space cost billions if not trillions of US dollars.
"If you were going to put together this kind of space force, well, outer space has a particular detrimental impact on the human body from the point of the muscles exposure to radiation etc."
There was also space tourism and the implications of where the liability landed if someone was injured while on a commercial trip, and would it mean the need to set up a Space Law Court.
But as for now, her students appeared to be taking it in their stride.
"Some students thought they would be studying aliens and Darth Vader, what do you do if you meet Darth Vader in outer space," she laughed. "We do touch on issues like that where you do look at if conflict ever broke out in space."
They also looked at issues including owned the Moon and the mining of asteroids, meteors and other celestial bodies in the future.
"In fact, internationally, that technology is starting to be developed very, very quickly."
