It seems as though she can be claimed as your dependent. If so, her standard deduction is limited to earned income plus $400. Assuming that the $1,500 of income is earned income and less than half of her support, any amount of the Roth conversion over $400 will be taxable. Furthermore, any amount of the Roth conversion over $2,300 will be subject to kiddie tax at your tax rate.
(As Opus 17 indicated, it's unusual for a 20-year-old to have a traditional IRA balance of $20,000 unless, perhaps, it's the result of a rollover of a 401(k) where she made substantial elective deferrals. If it came from regular IRA contributions over at least 4 years, it seems that she would have made Roth IRA contributions rather than traditional IRA contributions.)
