Qatar does not have oil reserves. It does, however, have the largest natural gas reserves. This won't affect the price of oil, and since the price of natural gas is mostly local, it won't affect the price of natural gas here.
You are right about only Saudi has oil. Qatar has oodles of gas LNG being produced by ExxonMobil, Tillerson’s old company. KSA wants to IPO ARAMCO at the end of the year. What better way to drive up the price of oil than to have a stand-off, or even shooting war, with a Gulf neighbor? That puts hundreds of billions of dollars in play for KSA with their IPO, if the market becomes nervous about oil price. Plus, nat gas price goes up because the embargo/blocade of Qatar takes so much LNG off the market. This is a giant chess game. Following the Trump visit to KSA, and sale of more arms, KSA suddenly becomes aware and upset that qatar supports Hamas (Iran’s friend) and that Al Jazeera says terrorist supporting things! Shocked, I tell you. Qui bono?