Here is the sort of story which is only ever going to turn up in an anthology written by and for fans. It isn't fan fiction, as such, but it is fanwank. This story is, basically, the Brigadier (retired) meets the First Doctor and Susan before the First Doctor has met the Brigadier in his own timeline, as it were. And Doris is there too.

There's not a lot else going on. The Brig has a boat with which he rescues Susan from the middle of a lake. The Doctor pretends he doesn't know the Brigadier, but does actually because he's been to the Brigadier's funeral, in the future (which all the Doctor's attended). The Brigadier mentions having met the First Doctor in The Five Doctors but doesn't mention The Three Doctors. The Doctor leaves having warned the Brig to get rid of his boat.

It's nicely written but slight and I'm not 100% sure what the point of the story was aside from being a proper meeting between the Brig and the First Doctor. A Christmas present for the fans maybe.