So. Is it?
My daughters are 13, 12 (twins), and 8. They enjoy fantasy, cartoons, and pop fiction. My spouse and I are fairly conservative in what we permit them to view.
My six year old watches it with me. There are things he sometimes find scary (usually thanks to the music, and suspense rather than what something looks like), but kids should be allowed to be scared. He occasionally gets nightmares, but nothing he has seen has kept him up all night, he normally falls straight to sleep after waking. More often he pretends to be the monsters, his current favourite is pretending to be the monster under the bed and grabbing my ankle (from the most recent season). He likes to point out weeping angels when we walk past churches. We recently went to the Doctor Who Experience in Cardiff.
There are occasionally things that some more conservative parents might object to, for example two occasional characters are lesbians married to each other (one of who is a lizard creature the other human), in the latest season
they were seen to kiss. This lead to a total of six complaints in the UK. One returning character from earlier seasons was bi-sexual, really only reflected in how he would flirt with anyone attractive he came across. However most of the time this stuff doesn't come up that much in the series, and there is no on screen nudity.
Deaths tend to be bloodless, bodies turned to ashes on occasions, saying that the most recent season, did show a badly burned hand at one point.
They're allowed to read whatever they wish, but we limit what they see. We didn't, by way of example, permit them to see Firefly.
Yeah that sort of raised issues about prostitution every episode thanks to one of the characters.
I've never seen Dr. Who, but it sounds like something my spouse and I would enjoy. If it's kid-appropriate, we can watch with the girls and enjoy it as a family. If it's not, ok, but my husband and I will have to watch after hours.
It is intended as family viewing but I imagine you are getting it through some sort of on demand service? I suggest you watch a couple of episodes first to see what you think.