Woman Time Lords can control the way they will look when they regenerate, while male Time Lords cannot. This was established in Classic Who, when Romana regenerated.
Also, the Doctor wanting to be Ginger is not about the hair color. In Gallifrey, the only ones to have red hair were the people called Heroes which were beings who were time-sentient (meaning they could see all of the time at the same time). So I doubt they will ever make him ginger.
And on this episode of ‘Tearless makes a really obscure reference no one else in the house will possibly get’… I have done this instead of working on commissions, which I will now get back to.
I’m just going to leave it there and see how long it takes to be noticed.
(it’s taped on paper bits, by the way)