I agree that she should register her business in NJ where she conducts business. If, she's going to register as a SMLLC or other entity. I'd also think that hair dressing requires some state licensing and maybe local health department fees/paperwork. Again, in NJ where the business will be conducted.
If her biz is a NJ entity, the entity will file a NJ return. Then, unless a C-corporation, she'll have pass-through income to her federal return which results in a NJ non-resident personal return as well as her PA personal return. If a C-corp, she'll have a W-2 from NJ and still have the NJ NR and PA resident.
As Judy says, the SMLLC won't give her much legal protection, especially since she's the one providing the services. So, she'll want a good insurance policy on her business (no matter what form it takes) in NJ.
It's so much easier to "go up the ladder" to a more structured entity as time goes on and needs change. But, "going back down the ladder" usually has a tax impact if she decides later that she doesn't want the extra reporting requirements, costs, whatever of a formal entity.
In fact, going from an employee to a business owner is a leap in the best of times. Has she really thought through what adding a new state into her regulatory and reporting mix will cost her in time and money?