I've always thought with crossovers that if they're done well it shouldn't really matter if you're not familiar with one of the fandoms. For example, my favourite ever crossover is When Hellmouths Collide by Kimberley Rector and Martha Wilson. It's a Buffy/Xena/Hercules crossover and I've not seen a single episode of the other shows, but it's just brilliant and a super example of a great ensemble story where everyone gets their time in the spotlight. I highly recommend it if you haven't come across it.

In the meantime, I hope you enjoy that Dr Who crossover. As you say, it's beergood so you know it's got a great pedigree! :)