Carl
Level 15

Deductions & credits

Then she is self-employed and will need to file her own separate tax return, which will include a SCH C. When she starts her return, she must select the option for "I can be claimed on someone else's tax return". If she does not select this, then you will not be able to claim her as your dependent. It will have no effect on contributions to her ROTH.
Understand that contributions to a ROTH are ***NOT*** tax deferred. So she will pay taxes on any income in excess of $6400. The maximum amount that she can contribute to her ROTH is the "LESSER" of $5,500 or what  she earns for the tax year.
Keep in mind also, that if she has more than $400 of self-employment income, then while she may not pay the regular income tax if the total earnings are under $6400, she *will* pay the additional 12.6% self-employment tax. So if she earns "exactly" $5500 for the year, that only leaves $4807 to contribute to the ROTH after paying the $693 self-employment tax.
The self-employment tax is basically the employer side of social security and Medicare.