Doctor Who is not fantasy. It's science fiction.
I'm a Whovian, but seriusly.
OK, so, my bona fides is that I have about 70% of the extant original series material on DVD, and ALL of the new series on Blu-Ray. I'd kind of consider myself an expert on Who lore.
In the past there have been stories that were more sci-fi, but it was always a pretty light touch. Especially in the new series, there's a lot more fantasy than there is actual science fiction. Like, ok there's space...and...well that's about it. Fantasy travels to other worlds, gives us magic, constructs elaborate mythologies. Sci-Fi informs us how it would work with science (something Who never EVER really does) and usually has some moralistic tone about how these concepts affect, or could affect, our lives.
It's about as SF as Narnia.
However, it is decidedly not a traditional medieval magical fantasy series.