There are tourists in Qatar, I’m sure they get by somehow and also there’s always google translate. They might even have a hotel in the airport or very close to it. The most important part is that you don’t need a visa to exit the airport
I’m not familiar with Pakistan immigration and returning LPRs. If they do track it, then I would definitely get a separate ticket for Qatar (maybe even roundtrip) and then a separate one to the US.