If it is your child's business, they report the business on their own tax return.
Their net earnings from the business (usually the business profit minus the 1/2 SE tax deduction) is "compensation" that qualifies for an IRA contribution.
If you have a Partnership (you said "we" own an Etsy shop) that you are also an owner of the business, then the business needs to file a separate tax return on Form 1065. Your child's share of the business profit follows the same rules as I mentioned in the previous paragraph.
