Hi A.,
I'm not sure what your question is...... This is the land of opportunity. However, if she is going to be legally employed in the US, then she needs to somehow become a legal citizen so she can pay taxes.
If your question is will she be able to work illegally as a singer - I don't know the answer to that question - probably she will have difficulty as employers can face fines for hiring someone 'under the table'.
I don't think she will be able to have any type of career if she is not a legal resident or us citizen. There are many benefits to becoming a legal resident - even if she ends up to not have a singing career, so you should research how to go about getting her citizenship.
Edited to add
to Denise P: Ummmm, I have left my house lately - and I DO see the amount of illegal immigrants who are working and NOT paying taxes. But they aren't trying to have a singing career. If her question was "my daughter wants to work at the carwash down the street. do you think she can do that without being a legal us resident" I would have had a different answer. My answer was if she wants a LEGAL career she will have to pay taxes.
The illegal citizens who don't pay taxes aren't LEGALLY employed and therefore don't have ALL the opportunities that legal residents have. Along with that comes the responsibility to pay taxes.
and to A. - I doubt the music company will 'help' her with citizenship unless she has the voice of Charlotte Church, Celine Dion or Mariah Carey. Even then, singers these days are a dime a dozen and they will want someone who doesn't have legal constraints that make them do extra work. Additionally, she would have to 'prove' herself before they will take her on - and that will be hard to do without residency/visa/citizenship.
Good Luck