The basic dynamic of the region is that everywhere except Iran is a Sunni dictatorship with an oppressed Shia minority (except Iraq, which was a Sunni dictatorship with an oppressed Shia majority, and is now chaos). Iran does fund Shia resistance groups across the region, for obvious reasons.
Qatar is unusual in that it is the only Sunni nation to maintain good relations with Iran, because it seeks leverage against Saudi domination. They also may be involved in supporting assorted militants within Syria etc.
The Saudis routinely accuse Qatar of “supporting terrorism”; hence the supposed justification for the recent Saudi-led embargo against Qatar. The actual motivation likely had more to do with a desire to silence al-Jazeera.
Daesh, of course, is primarily backed by the Saudis. It was created to disrupt the potential of a Shia-controlled Iraqi rival to Saudi Arabia.