City Council Speaker Christine Quinn is out of the gate far ahead of her probable rivals when it comes to fund-raising for the 2013 mayoral race — and she didn’t even have to throw herself a birthday party to get there. Quinn has, in fact, raised enough money to match the limit she’s allowed to spend in the primary race in order to get public financing. She’s at more than $4.9 million right now, and the city’s contributions will bring her up to $6,729,000. She’ll still keep fund-raising, in case she needs the cash for a runoff election. And she’ll also focus on getting small (sub-$175) donations from New Yorkers, which, under the city’s campaign finance rules, allow her to get more matching money. (She can spend that in the primary; it’s the other stuff she raised herself for which she’s reached the limit.) But the pressure’s off on the financial front for Quinn — cementing her front-runner status even more solidly.