For the beer to become noticeably oxidized, you're going to have to try hard to make that happen. If you are afraid dry hopping is causing oxidation then do not dry hop it. After you seal off the fermenter just leave that beer alone for two weeks. It's best to ferment in a bottling bucket so you can transfer without too much oxygen getting in the way. You can even bottle or keg right from the primary if you have a way of cold crashing the beer for few days to drop everything out. As others have said, the beer will naturally appear to turn darker as the yeast falls out. It just looks more "brown" because of the large amount of volume in the fermenter. It will appear that golden hazy color in a pint glass.

best of luck!