Rather amusingly, I gave her a collection of Dalek fridge magnets. We have this knack of getting each other almost identical presents - or indeed identical presents, as happened one year when we gave each other the same book!
I commented to her that what it really needed was to be radio-controlled so it can scurry around yelling "Exterminate!" at everyone. Given the amount of miniaturisation these days there should be easily enough space to fit the necessary gubbins (battery, motors, controller board) in something that small.
Anyway, the other day I went digging through one of the many collections of random junk and came up with this:
It's the somewhat sorry-looking remains of a micro R/C car that I was given many years ago. I checked the size and the axle width is indeed smaller than the base of the Dalek, so I reckon with some creative reshaping of both car and Dalek it can be made to fit. Getting the steering to work will require some thought - the Dalek has a caster for steering, while this has a proper steering rack but is missing the spring that centres it. There's also not enough space to fit the complete car body as-is. Still, these are solvable problems and there's definitely enough space inside the Dalek to move the controller board and battery higher up.
Who knows? Perhaps on a rainy weekend I might sit down and see if I can make something of the two!