Yes. My husband and I filed our federal refund jointly (mind you he was behind 3K on child support) and they took it all of what he owed. BUT, I went back and filed out an 'Injured Spouse Form' to get back what i earned.
Yes, the IRS can intercept your tax refund for back taxes owed; also if you have government student loans that you owe on and also the child support division can intercept you refund for back child support owed.
I presume you mean your return showed a "refund" of 1079. Presuming your back child support is in their system, and it is more than the refund, the entire refund will be applied against it. Any reason it shouldn't be?
If you file joint and your tax refund gets intercepted, then you would have to file a "wounded spouse" form to get your portion of the refund. But beware, the child support office could hold the refund up to 6 months to clear all the paperwork before you get anything back.