My daughter's employer doesn't take out taxes.

1099 form. Stat !

They intend to 1099 her at the end of the year...that will also be reported to the government, and she is considered an "Independent Contractor"....Their accountants will prepare the paperwork, mail her a copy in January and inform the government...
She should be saving out 30% of her paycheck, whether it is cash, or check, for probable taxes...She will be required to file a tax return...but may not have to pay any or little if her yearly income is not enough to qualify...OR they may choose to pay her cash and not report it at all...this is something you need to know for sure, and should find out the details from an accountant...At the very least, she should keep a notebook of her income totals...BUT, she has to know from them if they intend to 1099 her, so she can save out the money for taxes.

She will have to file a 1099 for feds and do not know your state forms - she will need to set aside her guesstaments tax burden - I suspect she will end up paying next to nothing, but wise to set aside the money and then celebrate if she gets to keep it.

A place of business does not have to take out taxes. Actually it falls on the worker as long as they provide a 1099. If the place of business does not provide a 1099, she still needs to keep tack, if she gets a audit. It is not the business that will be effected. By the way you did not say her age.

She just turned 21.

Then she need to plan ahead for tax time.