She served as captain of the Slovak national team in the women's ice hockey tournament at the 2010 Olympic Winter Games in Vancouver.

All three continued their careers by playing hockey in Saskatchewan for head coach Barrett Kropf at Caronport High School in 2004.

She was part of the Slovak roster that defeated Bulgaria by an 82–0 score in September 2008 in the Olympic Pre-Qualification tournament in Latvia.

She was part of the Slovak team that qualified for the top division of the 2011 World Women's Championships.

In the second game, Veličková beat Daria Obydennova for the only goal in the shootout as Slovakia won the relegation series.