I'm not a tax expert, but I have done contract work and filed quarterly taxes. Quarterly taxes need to be paid Jan 15th for the previous quarter (4th quarter 2012), and on Apr. 15th for 1st quarter 2013. Penalties apply on your 2012 return not only if you didn't pay enough taxes for the previous year, but if you didn't pace the quarterly payments properly. In other words, if you earned all your money the first half of the year, and didn't pay the appropriate amount of tax during the first two quarterly payments, you will owe a penalty even if you make the payment in January. And don't forget you have to add social security and medicare for both the employer and employee rates. If you're already in the 15% bracket, that adds up to approximately 30% of whatever you earn, minus deductions. If your taxes are higher than what you owed the previous year, you do get a break from the penalties.
I had contract work that started in July one year, started paying taxes in September, and Turbotax tried to make me pay the penalty because it assumed I earned the money throughout the year. I had to really dig to find the form I knew existed to show how my earnings were distributed.
As you can see, it gets complicated. If this is your first time self-employed, you may want to find a tax expert. If she can find legitimate deductions for the contract work, she could earn her fee many times over.