At the Juniores level Donna Vekić reached 21st place in the standings, reaching the quarter finals at Wimbledon in singular and up to the semifinals at Roland Garros in double with Aljaksandra Sasnovič.
Among the professionals gets an important result at Tashkent Open 2012: after qualifying, she reaches to the final where she surrenders with a double 6-4 to Irina-Camelia Begu.
She made her debut in Slam tournaments at the Australian Open 2013 where she passed the first round defeating Andrea Hlaváčková but surrendered to the next match against former number one in the world Caroline Wozniacki.
On June 16, 2013 lost the Birmingham tournament finals against Slovakian Daniela Hantuchová in two sets.
In Fed Cup she played a total of three matches for the Croatian team winning one of those matches.
She succeeds in winning the first title in April 2014 by winning the Kuala Lumpur tournament against Slovak Dominika Cibulková.