Even worse scenario. The Daleks conquer Tubbieland. For some mysterious reason the Teletubbies were found useful for the Dalek Empire. Over a period of ten years, the Teletubbies have infiltrated the Dalek hierarchy, from the lowest worker to an advisor to the Emperor Dalek.
When the Movelans release thier anti-Dalek bioweapon, the Dalek Empire collapsed. The many slave races either died out or survived. A few went out to establish thier own empires.
One of the most successful races were the Teletubbies. They first stabilised the worlds that they were involved in administering. Later they started campaigns (so called "Let's be Friends and Live Together" Wars) to unite the Dalek Fragments and other worlds into the Tubbie Union.
Thier primary weapons were brain-rotting, Cuteness and gene-engineered Boo-Bah shock troopers.
The career of several teletubbies xeno-specialist Timelords careers were wrecked from this turn of events.