If your niece wishes to become self employed she needs to register with HMRC they may not accept she is self employed unless she is working for a minimum of two quite separate people or companies who should have no connection with each other. If she can show this to be the case, or she is actively seeking new customers, there should be no difficulty. She should submit an Invoice to you on a regular basis for work completed, if agreed you should pay the invoice within the agreed terms. I am assuming you are not thinking about Carer’s Allowance and your niece will not be registered for VAT, threshold £73,000.
HMRC have an advice team who are usually helpful.