My daughter made less than $2600.00 and didn't have any federal or state taxes taken out. She doesn't owe any tax. Does she need to file taxes?

It depends.

If her earnings were reported on a W-2, then, correct, she does not need to file a federal tax return. 

If her earnings were reported on a 1099 MISC, then she DOES need to file a return as self-employment taxes will be due on the income.

It depends, if she received W-2 no she does not need to file but if she received 1099-Misc yes she needs to file. You can also check this link to determine if she needs to file 

https://ttlc.intuit.com/replies/3302274