The US chief diplomat's three-day trip, which will also take her to Saudi Arabia, is aimed at enlisting broad regional support, including from Turkey, in a drive to stop Iran's sensitive nuclear work, her aides told reporters.
Clinton's mission comes amid a US security buildup involving the deployment of anti-missile systems to the Gulf as well as a flurry of visits to the region by senior US diplomats and military officials.
As well as meetings with Qatari leaders, Clinton was due to hold talks with Turkish Prime Minister Recep Tayyip Erdogan whose country has good ties with Iran and has repeatedly offered to serve as mediator on the nuclear issue.
"We obviously need to have Turkey's support as we move forward and contemplate particular actions on the pressure track," Clinton's spokesman Philip Crowley said.
Turkey's Foreign Minister Ahmet Davutoglu is due to visit Iran next week to push for a diplomatic solution to the standoff over Iran's refusal to suspend uranium enrichment.
The sensitive process, which makes fuel for nuclear reactors but in highly extended form can also produce the fissile core of an atomic bomb, lies at the centre of Western fears that Iran is concealing a drive for a weapon, something Tehran strongly denies.
Ahead of his talks with Clinton, Erdogan said Turkey was willing to serve as the venue for an exchange of Iranian nuclear fuel in any settlement between Tehran and the West.
"The International Atomic Energy Agency has said Turkey could serve as the centre for the exchange of uranium … but there is no agreement up until now," he told a Doha press conference.
Iran, which rejects accusations of seeking to build a nuclear bomb, said last Tuesday that it has started the process of producing 20 percent enriched uranium, defying Western threats of fresh sanctions.
The move came amid deadlock over a UN-drafted proposal for Iran to ship its low-enriched uranium (LEU) abroad in return for higher grade nuclear fuel from France and Russia for a Tehran medical research reactor.
Although Iran has said it is ready "in principle" to sign on to the proposal, it insists that not all its LEU be shipped out in one go as world powers are demanding.
It has also been insisting that the exchange take place on its own soil and has so far rejected a proposal by the UN nuclear watchdog that it send its LEU stocks to a third country.
Turkey insists the row can still be resolved through dialogue and argues that economic sanctions or military action against Iran would have a damaging impact on the whole region.
China has taken a similar stand and is now the strongest holdout to sanctions among the five veto-wielding permanent members of the UN Security Council.
On the second leg of her tour on Monday, Clinton will press Saudi officials to use their influence with Beijing to secure a change of heart, aides said.
But they neither confirmed nor denied suggestions that she would ask Saudi leaders to offer China, which imports much of its oil from Iran, supply guarantees in return for Beijing's support for new UN sanctions.
"Saudi Arabia has an important trading relationship with China already," Jeffrey Feltman, Clinton's top assistant for the Middle East, told reporters en route to Doha, via Shannon, Ireland.
Feltman noted that there have been a number of recent visits between the Gulf and China.
"We would expect them (the Saudis) to use these visits, to use their relationship in ways that can help increase the pressure that Iran feels," said Feltman, the assistant secretary of state for Near East Affairs.
Aaron David Miller, a Middle East advisor in past US administrations, doubts the Saudis would offer oil guarantees to China, whose economy is growing rapidly, to encourage Beijing to change its stance on sanctions.
Miller told AFP that US-Saudi ties have eroded since the September 11, 2001 attacks — which involved many Saudi members of Al-Qaeda — and Obama has disappointed Riyadh with his failure so far to revive Middle East peace talks.
During her tour, Clinton is also to address the US-Islamic World Forum, building on President Barack Obama's own speech in Cairo last year calling for a "new beginning" with Muslim communities worldwide.
She will also meet the board of the Qatar-based satellite television Al-Jazeera — a repeated target of US criticism.
