Mothers want what is the best for their children. Now, with the help of e-commerce platforms, Chinese mothers can buy imported infant products hand-chosen by the daughter of a former Australian prime minister.

Jessica Rudd, whose father Kevin Rudd was Australian PM between 2007 and 2010 and again in 2013, recently opened a store on e-commerce giant Alibaba Group Holding Ltd's platform.

The store, called Jessica's Suitcase, was set up on Tmall Global, a dedicated online platform helping overseas merchants sell to China, and mainly sells organic baby food and women's goods from Australia, including fruit purees and sanitary pads. The best-selling products for now is paw paw & honey balm with online records showing sales of at least 856 items by last Friday.

Rudd, the mother of a three-year-old, announced the opening of the store last Wednesday through her Weibo, or micro blog, account. "I hope you will like Jessica's Suitcase and find what you need in it!" she wrote.

Her father helped promote the business by forwarding and commenting on her Weibo message: "Good to see my daughter open an online store in Tmall and sell Australian specialties."

The news has also interested many Chinese Weibo users. "Competition in the daigou business (means hiring someone overseas to shop for certain products) is getting more intense," one user said.

"It seems the rule of daddy-is-the-key also works in the business of daigou," another commented.

Rudd said that she is focused on making her venture the best online store. "It doesn't matter whose daughter you are, every Tmall Global flagship store has a responsibility to their loyal customers and that is a role I take very seriously. I am honored that Jessica's Suitcase has been supported by over 19,000 shoppers already in three days, but I know I have to earn their trust. I am an online shopper too," she said in an email to China Daily.

Last year, Australian Organic appointed Jessica Rudd as "trade ambassador" to help increase organic trade between China and Australia. She has lived in Beijing for five years and is married to an immigrant from Hong Kong.

Rudd is one of the growing numbers of high-profile overseas vendors, who are seeking access to China's large and rapidly growing middle-class consumers via online channels. British soccer star David Beckham launched a Tmall flagship store for his whisky brand, Haig Club, late last year.

With Chinese consumers getting more sophisticated, they want non-standardized and customized products from all corners of the world, said Li Yang, assistant professor of marketing at Cheung Kong Graduate School of Business. Li said that with such a large demand, global procurement is taking place not just in brick-and-mortar stores but also online.

According to a recent report on cross-border e-commerce by multinational consultancy Accenture, China is expected to become the world's biggest cross-border business-to-customer market by 2020.

To capitalize on the cross-border e-commerce wave, Alibaba has been aggressively promoting the growth of cross-border online shopping with government officials and business leaders around the world. Earlier this month, Alibaba Executive Chairman Jack Ma visited the United States to talk about the company's international strategy and how small businesses can use the Web to sell directly to Chinese consumers, who are increasingly looking for high quality, imported products.

Yang Ziman contributed to this story.