Highlights - Rising star Gauff beats Ostapenko to win first WTA title
But she won't be able to play week in, week out on the tour for another couple of years.
That's because of the rules the WTA have about the age of their players.
At the age of 15, a player is allowed to participate in ten professional tennis tournaments, plus the year-end Finals or Elite Trophy should she qualify - and she's also allowed to play in the Fed Cup if selected. She can also pick up three wild cards over the course of those 12 months.
Once she turns 16, she's permitted to play in two more pro tournaments than she was the year before - and gets one more wild card.
A 17-year-old player can participate in 16 pro tournaments and now gets the maximum possible wild cards - and once she turns 18, those restrictions are lifted entirely.
The idea is to protect young players - and to protect them from a variety of factors. It's tough enough dealing with media spotlight, commercial demands, your team and family's expectations when you're an adult; it's even tougher when you're a legal child, and also still developing physically. (The physical stress of playing week in, week out on the tour cannot be underestimated now; it is clear that tennis has become a more and more destructive game to the body in recent years.)
Yes, there have been plenty of teenage phenomena in women's tennis - but plenty of them have burnt out pretty quickly. Martina Hingis was world number one at the age of 16, and retired due to injury at the age of 22 (although she did make a later comeback where she concentrated mostly on doubles). Anna Kournikova made her Fed Cup debut when she was 14, and by the age of 22 a succession of back injuries had forced her out of her career. And by all means point to the Williams sisters as potential teenage role models, because both of them won Grand Slam singles and doubles titles before their 21st birthdays - but both were protected in their earliest professional years, staggering their entries into tournaments, and sometimes even opting to play qualifiers rather than pick up wild cards, because that experience was better for their overall game.
Gauff secures first win against top-10 opponent when sinking Bertens
For age-rule sceptics, it's worth considering the records that Gauff is breaking. She is the youngest singles champion on the WTA Tour since Nicole Vaidisova in 2004. By 2010, the Czech had retired. Aged only 20, she said she was fed up with playing tennis.
It is also worth considering Gauff's results in context; she actually lost in qualifiers in Linz, but got through to the main draw as a lucky loser.
American observers have been tracking Gauff's progress for some years, alongside that of a slightly older peer, Amanda Anisimova, and worrying that the strict WTA rules would hamper the youngsters' progress, prohibiting them from competing at their true level.
With both girls picking up their maiden titles in 2019 as well as impressing at Grand Slam level, it seems that being shielded just a little bit from the spotlight is not doing them too much harm at all.