"He runs with his dog before he reads the newspaper."
Translation:Hij rent met zijn hond, voordat hij de krant leest.
Indeed it is correct, but keep in mind that that actually has a different meaning. Met de hond rennen normally means the person is leading (the dog could be on a leash), can be used as roughly a synonym to de hond uitlaten (letting out the dog). But with met de hond meerennen (lit. run along with the dog) the dog is the one that is leading.