* US stocks up on earnings, Dow sees best month since Dec
* U.S. dollar index <.DXY> at 3-year low
* Euro zone inflation above expectations, bolstering euro
* Oil near 31-year peak, gold at all-time high
(Recasts and updates with U.S. markets' open; changes dateline to NEW YORK, previously LONDON)
By Barani Krishnan
NEW YORK, April 29 (Reuters) - U.S. stocks were steady early Friday, with the Dow Jones industrial average headed for its best month since December, while the dollar hit 3-year lows against a basket of major currencies.
Benchmark crude oil prices were above $125 barrel, near 31-month highs, as the tumbling dollar and violence in North Africa and the Middle East outweighed concerns about slowing economic growth in the United States.
Gold hit record peaks for a ninth time in the last 10 sessions, reaching near $1,540 an ounce.  [ ]
Robust U.S. corporate earnings, ample liquidity from the Federal Reserve, and the prospect of ultra-low interest rates for the rest of the year have driven stock prices higher recently, pushing the Nasdaq stock index to a 10-year high and the S&P 500 index up over 8.0 percent this year.
"There is a big bias towards the market going up and we've seen this through good news and what we would consider bad news," said Kim Caughey Forrest, senior equity research analyst at Fort Pitt Capital Group in Pittsburgh.
"The market kind of shrugs it all off and keeps marching higher."
The Dow Jones industrial average <> was up 35.04 points, or 0.27 percent, at 12,798.35 early Friday. The Standard & Poor's 500 Index <.SPX> was up 0.88 points, or 0.06 percent, at 1,361.36. The Nasdaq Composite Index < > was down 0.23 points, or 0.01 percent, at 2,872.30. [ ]
European shares gained just 0.1 percent following a six-session winning streak, with volumes crimped by a holiday in Britain for the royal wedding.
U.S. DOLLAR KEY TO APRIL MARKET GAINS
April's strength in equity and commodity markets came almost entirely from the slide in the dollar after Standard & Poor's revised down its outlook for the U.S. sovereign credit rating the Federal Reserve's admission that it was more concerned about economic recovery than the greenback's resilience.
"It's still a story of general dollar weakness," said Richard Wiltshire, chief FX broker at ETX Capital. "Markets are pretty thin and there's not a lot of depth to them." 
The U.S. dollar index versus major currencies <.DXY> fell as low as 72.850, the lowest since 2008.
The euro <EUR=> neared a 17-month low against the greenback, trading at $1.4870 by 1200 GMT.
Inflation in the 17-nation euro zone bloc edged up to 2.8 percent in April, well above the 2.0 percent target ceiling of the European Central Bank, which raised interest rates for the first time in two years earlier this month. The latest inflation numbers raised prospects for another ECB interest rate rise soon. 
The Australian dollar <AUD=D4> soared to 29-year highs, hitting $1.0964. The Swis franc <CHF=> hit a record high of 0.8653.
The 19-commodity Reuters-Jefferies CRB index <.CRB>, a broad indicator of the commodity market, is up nearly 10 percent this year, making it the world's best performing asset group.
World equities as measured by the MSCI <.MIWD00000PUS> index are up by some 5.0 percent over the past two weeks, inching up again Friday.
The U.S. ten-year Treasury yield <US10YT=RR> was steady, but set to post its first monthly drop since August 2010 on expectations the Fed will keep near-zero interest rates for an extended period. 
* For Reuters Global Investing Blog, click on
* For the MacroScope Blog, click on
* For Hedge Fund Blog, click on
http://blogs.reuters.com/hedgehub (Additional reporting by Mike Peacock, Jessica Mortimer, Atul Prakash and William James in London; Ian Chua in Sydney; and Umesh Desai and Jongwoo Cheon in Singapore)