Can I claim married filing jointly?

Background: I am a U.S. citizen. I married with a J-1 visa student in Sept. 2006. J-1 status waived by U.S. govt in early summer 2007. Not completed any other change of status paperwork. Had child together Dec. 2007. Wife received no income in U.S. Her college tuition and fees paid by Thai government. Have 1099 for this money.

You can file either as Married Filing Jointly or Married Filing Separately.
On joint return you will get standard deduction of $10,700 and exemptions for all of you including your child. Then your spouse will also treated as resident and must pay FICA taxes. You can get tuition fee deduction and child tax credit.

All is true EXCEPT for the part of paying FICA taxes.

A recent IRS ruling says the wife can file jointly with her husband and STILL claim exemption from FICA based on her visa status; see link below.

Nonresident Spouse Treated as a Resident