I am not normally a pronunciation Nazi. But this Explainer from Slate gets one thing wrong (by omission). The pronunciation of Qatar is not "cutter" but rather "Qutter" - the Q here represents the hard qaf sound of Arabic rather than the soft ke. Think of qaf as the same thicker, glottal sound you see in the word "baroque". Plus, the first vowel is not just "uh" but more like "aw". And even the "t" is really softer, halfway between "t" and "th".
UPDATE: my mistake, and kudos to Slate. They did get it right, way back in December. They even have an audio link.