She hires the clothes out for four days at a time and prices per item range between $19 and $199.
Since the site started, Miss Aakarsha said she had 56 orders from women hiring her dresses, including a customer from Australia who paid extra shipping and ordered it for a week instead of four days.
Her collection includes the same dresses worn by singers Ariana Grande, Cassie and Nicole Scherzinger and Kim Kardashian's youngest sister Kylie Jenner.
Miss Aakarsha hopes to expand her collection as the site becomes more popular and purchase dresses at wholesale price direct from designers.
"It's a win-win situation for everyone," Miss Aakarsha said.
"You don't have to spend $800 on a dress only to wear it once."
Aanya Rana, 19, hired a $300 Shakuhachi dress for $70 from Rent the Trend for a concert.
"I don't feel it is necessary to pay for a dress when I only want to wear it once ... I would hire again," she said.
A similar site is being run by Auckland sisters, nurse Lucy White, 24, and nutrition student Emily, 20.
The pair bought nine designer dresses last month to hire out on their new site Lend the Trend.
"We've had a pretty good response so far," Emily White said.
"My sister is a nurse and I'm a student so it's a good way to make some money on the side."
Donielle Brooke, a 22 -year-old hairdresser from Auckland, set up a Facebook page dedicated to selling and renting designer clothes.
She said the popularity was down to social media apps like Instagram.
"People that are like the It girls on Instagram post [designer clothes] on their Instagrams and other people see it and get inspired and want that same thing."
Her Designer Wardrobe page has more than 33,000 likes and her website, launched four months ago, had 2.5 million hits, she said.
"It's encouraging girls to be able to be a bit smarter with their money ... you don't need to have a wardrobe full of clothes any more, you can rent it out," she said.
Sarah Loggie, social media manager for marketing company Mosh, also put the growing popularity in designer rentals down to Instagram, as well as celebrities showing off their clothes on social media.
"There's a lot more focus on [Instagram] at the moment. Because we're in New Zealand and we're quite small, someone will do something on Instagram that gets a little bit of traction and the people in that kind of circle will copy it and then it will become really popular."
But Annette Jury, owner of Taupo formal-wear store, Dusk 2 Dawn, warned the clothing rental business may not be sustainable.
She hired out ball and formal dresses for seven years but recently stopped because they became damaged too quickly.
"You can only really do it if the fabrics are really good and are easy to clean ... otherwise customers start complaining of marks."