Heatherson progressed through the Charlton Athletic centre of excellence and was the reserves' top-scorer in 2001–02. On her full league debut in November 2003 she scored a hat-trick against Aston Villa, and finished the season with 12 goals from 12 starts. She was named FA Young Player of the Year in 2003–04 and won the League Cup. She played as Charlton lost the 2004 FA Women's Cup final 3–0 to rivals Arsenal, for whom Julie Fleeting scored a hat-trick. The next season she got a measure of revenge by scoring in Charlton's 1–0 FA Women's Community Shield win over Arsenal, then helping the club beat Everton 1–0 to win the 2005 FA Women's Cup. After suffering with injuries, Heatherson appeared as an 85th-minute substitute as Charlton lost the 2007 FA Women's Cup final to quadruple-winning Arsenal. When Charlton Athletic withdrew their women's club's funding that summer, Heatherson joined the player exodus and turned out for the Icelandic club Stjarnan. She then joined Southern DivisionWFC Fulham ahead of 2007–08, scoring 16 goals in four pre-season friendlies. Heatherson finished as the Southern Division top-scorer but broke her shin towards the end of the season. After Fulham's promotion, Heatherson rejected the chance to play with them in the top flight. She preferred to stay in the Southern Division with Millwall Lionesses, who were managed by her former Charlton Athletic manager, Keith Boanas. Heatherson's 20 goals in 20 games helped Millwall to promotion in 2008–09. Towards the end of the following season she signed for Chelsea, who had lost Lianne Sanderson to Women's Professional Soccer in the United States. Heatherson spent the 2010 summer season playing professionally with AmericanW-League club Buffalo Flash. She scored seven goals in nine matches as the Flash stayed unbeaten and won the league. In October 2010 Mark Sampson signed Heatherson for Bristol Academy ahead of their inaugural FA WSL campaign. She started both the 2011 and 2013 FA Women's Cup finals as Bristol lost 2–0 and 3–0, respectively, to Arsenal. The league restructure caused by the FA WSL's foundation meant Bristol qualified for the 2011–12 UEFA Women's Champions League as FA Women's Cup runners-up. Heatherson overcame her fear of flying to score in the away leg of the tie with Russians Energy Voronezh, but Bristol succumbed 5–3 on aggregate. In the 2013 FA WSL, Heatherson scored as Bristol recovered from 3–0 down at half-time to beat Doncaster Belles 4–3 and force a title decider against Liverpool on the final day of the season. Heatherson played as Bristol were beaten 2–0 at Liverpool, but they consoled themselves with another UEFA Women's Champions League qualification. Heatherson was released by Bristol Academy in June 2014, after falling out of favour. She retired from football, but was persuaded into a comeback with FA WSL 2 club Yeovil Town in December 2014.