Its misfortune is that its region is volatile and a theatre for competing global interests. It has giant neighbour Saudi Arabia hanging on its shoulder and Iran just across the waters of the Gulf. If Iran and the West came to blows, Qatar could be caught in the middle.
Which is where Beckham comes in. Qatar is using the globally understood language of sports - notably soccer - to put itself on the map, to buy friends and influence not only in the world's corridors of power but in its households, too.
The purchase of PSG, Qatar's winning bid to host the World Cup in 2022 and its investments in other sports ventures are not simply part of Qatar's forward-thinking efforts to secure alternate revenue before fossil fuels run out.
They are not designed solely to encourage Qataris to partake in sports instead of just watching them on their flat-screen TVs, nor merely vanity buys by wealthy sheikhs outshining each other.
Instead, experts say, Qatar is using sports to build itself into a globally recognised and respected brand.
Qatar used to be known for being unknown. But Iraq's 1990 invasion of Kuwait, also relatively small and backing on to the Gulf, and the potentially hostile geopolitical environment in which they live, have demonstrated to Qatari leaders that anonymity isn't their smartest policy option.
Becoming a player in sports is part of Qatar's efforts to anchor its future and security, not unlike the way in which a pufferfish swells into a ball to appear bigger and more formidable to predators.
"A defence by popularity, so to speak," said David Roberts, deputy director of the Qatar branch of RUSI, a British security think-tank.
"If you are going to be invaded by someone it seems to me that you want people to know damn well where you are," Roberts said. "You don't want people to go, 'Qatar? There's a country that begins with a Q? Where's that? Never heard of it."'
Should he join PSG, Beckham would be expected to bring worldwide attention and boosted revenue through merchandising and perhaps new sponsorship to Paris' leading soccer club, which is being pressured to quickly up its ante and produce results by its Qatari owners who bought a controlling stake in May.
French media reported that President Nicolas Sarkozy, without playing a direct role in the takeover, looked favourably on the sale, not least because it pumped much-needed funds into the club he supports.
Sarkozy has nurtured French relations with Qatar's ruling family and he has ties with PSG shareholder Sebastien Bazin.
Luc Dayan, who was involved in a 2006 effort by Qatar investors to buy PSG, said the purchase couldn't have happened without French political backing.
"A takeover like that in France, where everything is very politicised, cannot happen without political agreement at the highest levels," Dayan, former president and main shareholder of the Lille club, said.
The fund that bought a 70 per cent stake in PSG is controlled by Qatar's crown prince, Sheikh Tamim Bin Hamad Al Thani.
That, said Dayan, made this a "more political and strategic investment" than the Qatari takeover in 2010 of another struggling European club, Malaga, in Spain. The buyer then was Sheikh Abdullah Bin Nasser Al Thani, who is a member of Qatar's ruling clan.
So while it may appear from the outside that Qatar is making a land-grab in European soccer, its investments are not necessarily co-ordinated and unified.
"These are groups of different parts of the Qatari elite which are almost competing with each other to try to buy into Brand Qatar," Kristian Coates Ulrichsen, an expert on Gulf politics at the London School of Economics, said. "There's a lot of very ambitious sheikhs with a lot of money looking enviously around and seeing this guy's done this, this guy's done that, how can I get a slice of the action?" Beckham, on an Asian tour with his club, the Los Angeles Galaxy, is keeping people guessing about his intentions.
Re-signing with the MLS champions would spare his family from being uprooted from Los Angeles.
But PSG, which reportedly is offering millions, could offer a final bumper pay cheque and chance to show, at 36, that he can still compete in a European league, perhaps furthering his hopes of playing for Britain at next year's London Olympics.
"I'm very proud of the time that I've spent with the Galaxy and it might continue," he said last week. "I think at the end of the day I have a big decision to make, but I obviously haven't made one yet."
While PSG will hope Beckham's right foot can still conjure up his trademark free kicks and pinpoint crosses, he is too slow and fragile now to produce match-winning performances week-in, week-out.
But that won't matter so much if his star power helps lure other players to PSG and, most importantly, drives up interest in France and internationally in both PSG and the French league, which lags behind those in Spain, England, Germany and Italy.
Beckham's biggest value to Qatar lies in his glamour which would marry nicely with Paris' fame as the capital of chic, not in his fading soccer skills.
- AP