I need some audience participation here. The song came to me in a flash of inspiration, but I got only this far:

There’s a Dalek in my house
and I don’t know what to do
I know he wants to kill me,
‘cuz that’s what Daleks do

He always says “EXTERMINATE” and now that he can levitate, I can’t escape by climbing up the stairs!

So, feel free to make comments and suggestions, and maybe we can put this to music.