Interestingly - or not depending on your perspective - my kids watched MLP a long time before I did, I only started watching mid season 3, and I saw all of S4 before 1 & 2. When I did get around to watching 1/2 for the first time, it was not in chronological order (random episodes shown on a freeview channel here in the UK) and Sisterhooves Social was one of the last episodes I saw from the first 4 seasons. By the time I watched it, I already had my little headcanon re Derpy/Dinky, and Amethyst being Derpy's younger sister - I had already seen all of Dinky's scenes with Amethyst on youtube, So when I saw the scenes with Derpy that I posted above, I was very pleasantly suprised.
As far as the origins of it go, I always assumed it's due to Derpy's original canon name being Ditzy Doo, and Dinky's name being Dinky Doo. Related ponies don't always have the same last name - Like the Apple Jack, Apple Bloom and Big Mac, but some do - like the Pie family, and due to Ditzy and Dinky being rather similar words, going by standard kids show formula, it suggests very close relations.