The show could be announced immediately after the conclusion of Series 7 of Doctor Who and Season 1 could air in late summer as part of the 50th Anniversary celebrations. Right now, the only Doctor Who spin-off is Torchwood, which is currently dead in the water. They're going to need something new and fresh and exciting, and the end of The Doctor's Daughter just leaves one massive plot hole that needs filling.
Basically, it goes something like this. Jenny traveled back to 2005 Earth with a vortex manipulator she got from "some Stormcage inmate" (River Song) and got a job as a secret agent for Torchwood 1. Using her time traveler's knowledge of history, she managed to escape the Battle of Canary Wharf and the events of Children of Earth. She now lives in a London high-rise apartment with her completely ordinary roommate/lesbian girlfriend. Due to this being a children's show, the romantic involvement is minimized (she tells people she is in a relationship, but never says with whom, and she is strongly implied to be lesbian). She goes around eradicating minor alien invasions in Britain. She also sometimes has to stop humans from attacking aliens who simply crashed and have no understanding of Earth culture and thus did something offensive.
Sometime during season 2, she and her dad finally meet when they go after the same alien. After that episode, she continues, only with her own sonic screwdriver and the Doctor popping in once every now and then. The Doctor can explain to her that the reason she only partially regenerated was because she was only a few hours old. He could explain that regenerative functions don't fully take hold until age 3 or so.
She runs a website where people can report alien sightings and view advice on what to do in the event of an alien encounter. She makes money from the advertising revenue from that blog (plus her former massive Torchwood salary). This is also sometimes where she finds out about the alien for that episode.
I really hope someone from the BBC reads this, because this is one of my more serious proposals and could actually be made into a successful show. If they want the 50th Anniversary to be massive, I can see no better way than bringing back a Time Lady and giving her her own show.
