Does she have to buy the photoshop or is there a possibility to install PS with my account on her laptop?
By @maltje1962
Yes, she needs to buy her own subscription. See the legal terms here:
https://www.adobe.com/legal/terms.html

Here are the current plans. Choose Individual from the top Nav bar and Photo from the left Nav bar, then scroll to find the Photography plan that includes PS and LR.
https://www.adobe.com/creativecloud/plans.html
The Photography plan is annual and can be paid monthly or in a lump sum. There is a fee for early cancellation of an annual plan after 14 days.
(I'm mentioning the lump sum in case you are looking for a very last minute Christmas present. 😊)

Jane