How do we claim our child born in December as our dependent when we don't have her Social Security number?

You must enter her Social Security number on your tax return to claim her as a dependent. Apply for a Social Security number at the same time you apply for a birth certificate. If you do this, you will likely receive the Social Security number before the due date of the return, which is normally April 15th.  Although you can also claim a dependent with an Individual Tax Identification Number or Adoption Tax Identification Number, certain credits require that the dependent have a Social Security number.  See the Form 1040 instructions for additional information.