Do we qualify for the EITC since we made around $39,000 with a household size of 3?

Yes you may be.

What are the qualifications for the Earned Income Credit (EIC or EITC)?

• Have earned income.
• Have been a US citizen or resident alien for the entire tax year.
• Have a valid Social Security number (not an ITIN) for yourself, your spouse (if filing jointly), and any qualifying children on your return.
• Not have investment income exceeding $11,000.
• Not be filing a Form 2555 or 2555-EZ.
• File a return with the Single, Married Filing Jointly, Head of Household, or Qualifying Surviving Spouse filing status, even if you're not required to file a return.

In addition, both your earned income and Adjusted Gross Income (AGI) may not exceed:

• $17,640 if you're not claiming a qualifying child ($24,210 if filing jointly).
• $46,560 if you're claiming one qualifying child ($53,120 if filing jointly).
• $52,918 if you're claiming two qualifying children ($59,478 if filing jointly).
• $56,838 if you're claiming three or more qualifying children ($63,398 if filing jointly).

If you're not claiming a qualifying child:

• You (and your jointly filing spouse) can't be claimed as a qualifying child or dependent on anyone else's return.
• You must be at least age 25 but under age 65 (at least one spouse must meet the age rule).

Also, the IRS has a   EITC Assistant