Dobovšek, who started for the SK Triglav Kranj , began his international career in 2005 in FIS jumping in his home town of Kranj . In July 2007 he started jumping in the FIS Cup in Bischofshofen . In February 2008 he made it into the top ten for the first time in Szczyrk . In the overall standings he finished 74th at the end of the FIS Cup season. At the Slovenian Ski Jumping Championships in 2008 in Kranj, he reached third place with the team. In July 2008 he started in Kranj for the first time in the Ski Jumping Continental Cup , but was disqualified in his first competition. A year later in Velenje he was disqualified again. At the Slovenian Ski Jumping Championships 2010 in Kranj Dobovšek won the gold medal with the team. On January 16, 2010 in Titisee-Neustadt he finished a Continental Cup competition in 41st place for the first time. From July 2010 he jumped firmly in the Continental Cup and in September 2010 in Almaty reached the points for the first time with a 19th place.
At the Winter Universiade 2011 in Erzurum , Turkey , he was able to win the gold medal on both the normal and the large hill. With the Slovenian team, he also took second place in the team competition. A few days later he won an FIS Cup in his home town of Kranj. At the Continental Cup in Iron Mountain a week later, he achieved the first Continental Cup victory of his career. After further good performances in the Continental Cup, a few weeks later he was second again on the podium in Kuopio .