Can I claim my child for this years tax return? SHE WAS BORN JAN 4, 2012?

Not for 2011 tax year.

Try it, and you'll get a nice letter from the IRS.

You cannot claim your child who was born Jan. 4, 2012 on your 2011 tax return. You will need to wait and claim her for the first time next year.

You can claim your child on your 2012 tax return since she was born in 2012. You cannot claim her on your 2011 tax return since she was not born in 2011.

Yes you can. This year is 2012 so she can be claimed on your 2012 tax return that you file in 2013.

The answer to the question that you meant to ask is no, you cannot claim the child on the tax return that you will be filing within the next few weeks. However, that is technically last year's tax return.

The answer to the question that you did ask is yes, you can claim the child when you file "this year's tax return", because "this year's tax return" is the one that you file next year. (Tax returns belong to the year when you earned the money reported on the return, not to the year when you file them.)

she was not born in 2011 and is not an exemption for 2011

Nope.