Flights to Israel but not UAE or KSA?
C'mon.
I believe it's the UAE that blockaded Qatar, the Qataris would be happy to have flights to the UAE. While it's true Qatar is closer to the shiite world of Iran, Turkey, Hamas, & Hezbollah, they have the best relationship with Israel with significant unpublished official visits, much like the UAE has been before the ultimate normalization.
Qatar finances Gaza at the behest of Israel since the US stopped their financing against Israeli request. Israel is mostly happy with the current status quo in Gaza, and every time the Qatari money runs out Hamas increases it's violence until Israel succeeds in persuading the Qataris to send more funds.
Qatar is forward thinking country that hosts 10k USA troops including the command for many middle east operations. It is in no way in Iran's pocket and normalization with Israel is definitely conceivable.