THE fairytale of New York didn't get its Hollywood ending.

But Laura Robson is determined she will go to the ball. The next steps in the 18-year-old's attempts to gatecrash the A-list of world tennis will be played out away from the glare of the cameras on the Asian subcontinent, as the teenager goes on a whistlestop tour of duty to Guangzhou, Tokyo, Beijing and Osaka. First, though, a quick burst of shopping therapy in New York City and a week of training at her Wimbledon home.

"I have to continue working hard and try and keep the level up in those four tournaments that I have done here," said Robson, whose 6-4, 6-4 defeat by reigning champion Sam Stosur came on the Australian's ninth match point, and after back-to-back wins against previous major winners Kim Clijsters and Li Na. "You know, I'll go into Guangzhou and Tokyo with a lot of confidence. I think the courts in Asia will suit me quite well because they're generally quite fast. I'm really looking forward to it."

Robson only started her new coaching arrangement with Zeljko Krajan at Cincinnati last month – Andy Murray's fitness coach Jez Green also helps her out with her movement – so plenty of the working arrangements remain to be thrashed out. She hinted last night that it could also involve time in Croatia. "We haven't done any training weeks for the moment, so we'll see how it goes," she said. "But I'm sure a fair few weeks will still be at home. If he [Krajan] needs to go see his daughter or something like that, then I'm more than happy to travel to Croatia."

The 18-year-old will pack plenty of positives in her luggage when she travels to Asia. Not only did her achievement here this week make her the first British woman since Jo Durie in 1991 to reach such a stage, Robson is already the highest-ranked teenager in women's tennis, and that ranking is projected to rise to at least the mid-70s. She has no particular figure in mind when she sets her rankings goal for the remainder of the year, but is comforted by the fact she has learned to live with the very best players in world tennis.

"I think the results will come as long as I keep working hard, so I'm not going to put a figure on it," Robson said. "I felt pretty good going into my first-round match. But I really wasn't looking past the first round. After Clijsters, I thought it was a great win, but I needed to back it up; that's what I did. I can definitely take the fact that, you know, I'm up there with the top girls in terms of level.

"I would love to continue playing in stadiums like that with a crowd like that, but I have to get my ranking up a bit more and keep working hard to get there."

In all likelihood, Robson has hit the big-time already. Judging by the support she has received on social network sites, the last week may have changed her life forever. "I've had loads of messages of support over the last few days," the said. "My phone has been running out of battery every few hours because there have been so many messages coming through. In the morning there was a camera crew outside my hotel, which was a little bit freaky. I got really excited because I thought they were waiting for someone who was actually famous. I didn't really think they were there for me at all until they started following me to the car."

The woman's singles competition continues apace without its newest star. Ana Ivanovic, the former world No.1, showed continued signs of her resurgence under Nigel Sears when she came through against an injury-affected Tsvetana Pironkova 6-0, 6-4 to reach her first grand slam quarter-final since winning the title at Roland Garros in 2008.

Things will get significantly tougher for the Serb in the next round, however, when she faces Serena Williams, who gave Andrea Hlavackova, the world No.82 from the Czech Republic, a brutal education, the dreaded double bagel completed in 57 minutes.

There was a shock of sorts when Sara Errani, the runner-up in this year's French Open, recorded a 7-6 (5), 6-3 win against Angelique Kerber, the German who reached the last four here last year, and has won more matches on the tour this year than any other woman.