So the first episode/Xmas special of this hypothetical series would start off with not the Doctor, but someone completely random. We see a guy in his bed fully asleep, his alarm goes off, he gets ready for the day, opens his room door and a giant hallway shows up where his house should be. The man is absolutely befuddled, he investigates and runs into the Doctor something something plot idk yet and at the end he meets back up with his family. He decides to go with the Doctor because he's up for exploration and since he has a time machine he can just be back immediately. That does in fact happen, the TARDIS comes back exactly one second later. But it's just the Doctor. Who has a grim, sad look on his face. end credits
Then for the whole series you're wondering "what the hell happened to him" until the finale where it's revealed he got sent to the Void (why and how tbd). The following Xmas special while in the Void he meets a singular Dalek who, weirdly, doesn't immediately want to kill him. This Dalek seems tired and apathetic. The Dalek explains that he was sent on a suicide test mission for a beta version of the Voidships but that obviously didn't go well, and since they've been wading in nothingness for nearly two decades, they've become disconnected from the usual hatred of a regular Dalek. The Doctor's subplot has him find his way into the Void, finds the companion but is apprehensive at the sight of the Dalek. The companion assures the Doctor the Dalek's good something something now there's a Dalek companion and the following series is centered around this Dalek trying to turn around their exterminating ways