You should be honest and report all income when applying for public assistance. Fraud is basically hidden lying, cheating and/or stealing. Intentionally not reporting thousands of dollars of income to make it look like you qualify for benefits sounds like that, no? If you are caught, you could lose future benefits, and possibly face criminal prosecution. Penalties vary by state, but you can avoid this by doing the right thing and report honestly and fully. Tahlequah is at the end of the "Trail of Tears" - don't start your own trail of tears by committing welfare fraud.
This is a general comment to your posting and is not meant to constitute legal opinion or advice. There is no attorney-client relationship in this matter. If you think you need legal advice or representation for this matter, you should consult a licensed attorney in your jurisdiction.