I would agree that Doctor Who does not have much awareness in the US. There's hardcore fans certainly and people who have a some knowledge of the show, but the vast majority of people would have no awareness of it at all or have maybe heard of the name of the show but don't know anything about it. It is no where near the level of cultural conscious you get in the UK where one might be aware of what a Dalek is even without watching the show.
The show has been only on BBC America and SyFy, both of which are stations that many Americans never turn on. And the old episodes were typically on PBS, which again, not very watched.
That all said, I do think a Doctor Who attraction would be a good addition for WDW if done well. It's the type of IP that can be enjoyable without knowing the source material and, conversely, the BBC could benefit significantly by exposing millions of new people to the show. There's been some mild cooperation already, with Disney selling Doctor Who merchandise at the UK pavilion in recent years.
(Complete aside, but when I was younger, my sister and I were super excited to buy Jelly Babies at the UK pavilion due to Doctor Who. They weren't exactly something you could find in the US easily.)
