Because of the World Cup, people who haven’t much focused on Qatar have been talking about, and there’s been a cottage industry of articles about how to pronounce it—and about how people are pronouncing it “wrong” or “incorrectly.”
Here’s my modest contribution: There is no one transnationally correct way of pronouncing “Qatar,” just as there is no one correct way of pronouncing “France,” or for that matter of pronouncing the name of the countries we call “Germany,” “Greece,” or “Russia.” Rather, each language has its own norms, which stem both from the sounds common in that language, and from the history of how a name has been adapted into the language. The “correct” way to call a country in a language is just a matter of what is customary in that language.
Thus, “France” is pronounced one way in French (with an “ah”) and another in English (with the more familiar English “a”). In Russian, it’s pronounced “Frahntsiya”; and that’s even apart from the fact that the “r” sounds are different in the three languages. I imagine many other languages have their own pronunciations.
“Russia” is likewise correctly pronounced in English as “Rusha,” though in Russian it’s “Rosiya” (I use italics to indicate emphasis) and in French it’s spelled “Russie” and pronounced “Roosee” (to use English transliteration), though with the different French R and “oo.” (It’s also “La Russie” in French, but that’s a separate matter.) And many countries’ names are completely different in English (or in other languages) than they are in the country’s official language; “Greece” in Greek is “Ellas,” and of course “Germany” in German is “Deutschland.” (Germany has many completely different names in different languages.)
Indeed, “England” in Arabic is, unsurprisingly, not “England,” but apparently “‘iinkiltira,” likely from the French “Angleterre.” I assume Qatari Arabic is the same on this point, though I recognize that there are some differences in how Arabic is spoken in different countries.
Are Qataris “wrong” if they call England “‘iinkiltira” while speaking Arabic? Not at all. Likewise, English speakers aren’t “wrong” when we pronounce “Qatar” in a way that’s normal in English (according to dictionary.com, that’s either kah-tahr or kuh–tahr).
Now if you want to pronounce Qatar the more Arabic way in English, for whatever reason (e.g., to impress people with your familiarity with the country), you should of course feel free to. But there’s nothing wrong in using the English name for a foreign country when speaking English, or the French name when speaking French, or the Arabic name when speaking Arabic.
For more on this as to Ukraine, Kiev, Turkey, and Moscow, see here.