No, either of you can report it if certain qualifications are met, but not both.
Form 1098-T - (I'm assuming it is 1098-T, since you have only mentioned 1098...) - parents report the education form, education expenses and claim an education credit if the child is claimed as their dependents. Otherwise, your daughter will claim the form and an education credit.
Form 1099-B - capital
gains/losses should be reported on the child's tax return, not the parent's.
Your daughter is required to file her own tax return if the unearned income (taxable
capital gain) is $1050 or more.
NOTES:
- If 1099-B is a consolidated statement and reports dividends (1099-div) on UGMA account, reporting depends on the unearned income amount. If your child's only income is unearned income not exceeding $1,050, it doesn't need to be reported. If your child's unearned income is $10,500 or more, she will need to file her own return. Unearned income amounts between $1,050 and $10,500 are reported either on your return or your child's return.
- For purposes of "kiddie tax" the child is defined as a dependent under the age of 19 (or under 24 if a full-time student) as of Dec 31, 2016.
