I'm no expert but his back end definitely looks weak. It's more than just a bum wiggle.
Dogs with hip dysplasia need to have good muscle to support the joints with as little extra weight as possible. 2 miles isn't a huge amount of exercise and I'm guessing it's on a lead so your challenge will be keeping him happy and content while managing him physically. If he's just a year he's still growing so you need to be extra careful. Did your vet say how bad it is? Would they consider operating? When our dog was diagnosed we got wetsuits and took him swimming and stopped all ball games and high impact exercise. It was a massive challenge having a young dog with H/D but you're in a better position to manage it if you find out early. Good luck.
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