So I haven't updated this book in a year and I haven't been planning to. However I do have two and a bit more stories about Kat that I wrote before the first chapter and were going to go in the book at a later stage. I've decided to post them now cause why not.
Any way just to make them make sense - Kat met the Doctor and has now figured out that she can travel through time and space without having to use a TARDIS or any other device. Then a while later she figures out that she can do more than that and actually travel into different worlds/universes which is where the people from Supernatural, Sherlock and a whole assortment of fictional worlds come in.
Basically the reason she can do all this is because she was created just before the war against the daleks by a time lord who didn't think they would survive the war. She was make to be a mixture of human and time lord so she can regenerate but she only has one heart and loads of other stuff. The time lord also took a part of a TARDIS's heart inside of her (kind of like when Rose did at Bad Wolf) but only the tiniest amount so it wouldn't kill her but she has some control over time and space aka. being able to change herself to whatever age she wants to be.
That's all I have to say really, if you don't understand something or I've accidentally left out a vital piece of info so that the whole thing doesn't make sense then tell me.