She was awarded the titles International Master (IM), in 2004, and Woman Grandmaster (WGM), in 2003, by FIDE.

She won the Austrian chess championship for girls, in various age groups, eight times.

Moser was awarded by FIDE the titles of Woman Grandmaster (WGM) in 2003 (Austria's first one) and International Master (IM) in 2004.

[6] Tournament victories include the Dresden women's event in 2000,[7][better source needed] Jena Open in 2009,[8] 2010,[9] 2011[10] and 2012,[11] and Chess Ladies Vienna in 2012[12] and 2013.

She used to play for the team Wolfsberg in Austria; and OSG Baden-Baden in the German Women's Chess Bundesliga, winning at least five times, and dominating for many years.