What?
Money earned for working is only ever reported on a tax return in that person's name, even if they are someone else's dependent. The only time you might report a dependent's income on a parent's tax return is limited circumstances with investments only.
Next, if you are paying your dependent for services performed, your dependent must file a tax return. Either they are self-employed/independent contractor, in which case they file a schedule C, or they receive a W-2.
You said "allowance." Paying your child allowance and calling it "compensation for work performed" to allow them to make Roth IRA contributions is tax fraud. If you are self-employed with a business of some kind, and you pay your child to work in that business, you would either issue them a W-2 or a 1099-NEC, depending on the type and manner of their work. If you are not a business, you can have a "household employee" if you pay them for legitimate services performed. If the amount is more than $2200, you must issue them a W-2. If they are your child under age 21, you don't have to pay household employee's tax.
https://www.irs.gov/taxtopics/tc756
https://www.irs.gov/publications/p926
An allowance is not wages for services performed. To prevent accusations of fraud if audited, you should carefully document the work your "household employee" does, and make sure you are in compliance with federal and state law. Under federal law, you don't have to pay minimum wage, but you must pay a "reasonable wage" for the work performed. But there may be state laws you must follow regarding wages, hours, and working conditions.
