I can't speak for your sister, only myself, but as an American I did not grow up with Doctor Who (plus I was born during the time it was in its hiatus anyways, wasn't alive during it's original run), but I might have seen a re-run ep or two as a kid on PBS, but I had no idea what it was or the back story it had.
I honestly did not really introduced to it until nuWho. I liked what I saw, so I made every effort to learn all about the original run of the show. I was lucky to meet someone at a LANNING event who had all the episodes of the original series, including the audio's and whatnot from the lost episodes. So thanks to that wonderful person, I was able to watch all the old episodes of every Doctor, up to the new series. So I have a good grasp on what Doctor Who is all about, and how it all works. I have to say, comparing nuWho to the old series is a bit more "whacky" and all over the place, it's faster paced that's for sure especially under Moffat. But I'm still able to grasp what is going on, but there has been some really big arcs that were just never that big in the old series. I mean, destroying the whole universe and re-birthing it, that's just really out there. Of course then I am reminded of the old serial where basically the Doctor started the Big Bang in the first place
But definitely things move at a faster pace now, than they did then. But also remember the serials of the old series lasted several episodes, so they were longer and more drawn out. I kinda look at the original series like it is more relaxed, and the new series is amped up more, faster paced, on adrenaline.