* Dollar tumbles 1.2 percent after dovish Fed * European shares rise almost 1 percent, Asian stocks gain * German Bunds track U.S. Treasuries higher * Commodities from oil to copper see gains By Marc Jones LONDON, July 11 (Reuters) - Shares and bonds rallied globally on Thursday and the dollar tumbled, after the head of the Federal Reserve signalled the U.S. central bank may not be as close to winding down its stimulus programme as markets had started to believe. This came despite minutes showing half of Fed policymakers think the programme should stop by the end of this year. As investors cheered the prospect of ongoing support, risk assets performed strongly. European bonds from Germany to Greece tracked gains in U.S. debt and European shares opened up almost 1 percent, pushing MSCI's world index, which tracks stocks in 45 countries, to its highest in almost a month. "Bernanke's comments were taken by the markets as much more dovish so I suspect it will be a good day for risk markets and I don't expect that to change in the near term," said Saxo bank Chairman and senior market analyst, Nick Beecroft. "We are still in a bit of a sweet spot for equity markets. The economy is doing well enough to encourage equity markets about future earnings, but not too hot to cause the Fed to remove accommodation." The dollar tumbled 1.2 percent against a basket of major currencies while the euro roared to a three-week high of $1.32085 at one stage, though it was back at $1.3038 by 0720 GMT. Copper prices gained 3.2 percent to exceed $7,000 a tonne, hitting a three-week high and extending the previous session's 1.4 percent rise as the dollar softened. Gold climbed 2.4 percent to a three-week high and was on track for a fourth straight day of gains while U.S. crude oil prices added 0.7 percent to their highest level since March 2012, extending Wednesday's 2.9 percent jump.