Inspired by Australian Test cricketer Shane Warne, Wellington taught herself to bowl leg spin in her backyard.[2] Wellington began her career playing for Port Adelaide Cricket Club. She rose to prominence in December 2011 when she was the player of the tournament in the national under-15 championships, playing for her home state of South Australia, and the next season she was selected to play for the South Australian Scorpions, South Australia's representative women's team. She made her debut for the Scorpions in the Women's National Cricket League (WNCL) at the age of 15 years and 150 days, becoming the youngest person, male or female, to represent South Australia in a senior match, breaking the record set by Clem Hill in the 1892–93 season, more than one hundred years earlier.[3] She proved her worth early in her state career, just a fortnight after her debut, helping South Australia to a win over Tasmania.[4] At the end of the 2012–13 season she had played 4 matches in the WNCL and 8 matches in the Australian Women's Twenty20 Cup with 10 wickets between the two formats.[5][6]
Wellington continued to play for the Scorpions in the following seasons, and in the 2014–15 season she gained the attention of the Cricket Australia Women's National Selection Panel. She was included in Australia's second XI team, the Shooting Stars, for their tour of Sri Lanka, on which they won every match.[7] She was then included in the Shooting Stars' squad for their trip to Dubai, where they played matches against the ECB Academy.[8]
After consistently strong form for the Scorpions and bowling figures of 3/13 in a Women's Big Bash League (WBBL) match for the Adelaide Strikers in the inaugural season of the tournament,[9] Wellington was selected to play for the Governor-General's XI in a tour match against India.[10] Her form continued to improve in the 2016–17 season and she was South Australia's leading run-scorer in grade cricket with 325 runs at an average of 81.25,[11] prompting selection in international matches for the first time.
On 24 November 2021, in the Eliminator match of the 2021–22 Women's Big Bash League season, Wellington took the best figures in the history of the WBBL, with five for eight from her four overs.[15] It was her 100th match in the WBBL, and she also took her 100th WBBL wicket in the game.[16]
Having become a regular member of Australia's national team, Wellington was given her first contract with Cricket Australia in April 2017.[26] Wellington was named in both Australia's ODI and Test squads for the 2017–18 Women's Ashes.[27] She made her Test debut for Australia against England Women on 9 November 2017 in the Women's Ashes.[28]
In December 2017, she was named as one of the players in the ICC Women's T20I Team of the Year.[29] In April 2018, she was one of the fourteen players to be awarded a national contract for the 2018–19 season by Cricket Australia.[30] In April 2019, Cricket Australia awarded her with a contract with the National Performance Squad ahead of the 2019–20 season.[31][32]