I lived / reapeatedly visited Qatar for almost 10 years. Sure, there were all kinds of older vehicles there, including old American cars. But you have to remember, that region only realized how wealthy they really were around the 70s. Then they started looking for a more luxurious type of lifestyle.
80's, 100's and 200's are ridiculously common over there. Also, they've had the 70 series "flatbed" in production since pretty much forever. Anything not suitable for regular use (old carbureted classics) probably ends up the same place all the other unwanted classics end up: junk yard or exported somewhere else.
Gulf arabs love their Toyotas, but the 100 and 200 series rule. If a Qatari family doesn't have at least one of those in the driveway, they are definitely an outlier compared to their peers. And they don't have the same kind of "expedition" mindset that some other people have. All they have is desert over there. It all looks the same and it's pretty dangerous if you get stranded. They need something dead reliable that can deal with the conditions, but they aren't big into camping if you know what I mean.