1. Maybe. Was the internship organized by her school and was it for credit? In that case, it is education and should be reported as "other income." However, if she was working at a company and not for school credit, then it should probably be reported as self-employment. (There is a lot of gray area here.)
2. The standard deduction for dependents is different than for non-dependents, see publication 501.
https://www.irs.gov/publications/p501
This is mostly to prevent parents from putting their investments in the name of their children and then having all the income be tax-free. If this is hobby or other income, then it is "unearned" income, and the standard deduction for unearned income is $1250, so a small portion of the $1500 will be taxable.
If you reported this as self-employment income, and she did not have other unearned income, then it would not be subject to income tax, but it would be subject to self-employment tax (about 15% of the $1500.)