Most likely, yes. Pink eye (conjunctivitis) is a catchall term for any infection of the eye or the membrane around it. The most common cause of pink eye is a bacterial infection that can spread to and from any species. Pink eye can also be caused by a viral infection (much less likely to spread) or a foreign object in the eye.
If the pink eye is not caused by a foreign object, then it is safest to assume it is the bacterial form and yes, you could easily give it to your dog. I'd recommend that anyone suffering from the infection avoid handling *any* family pets of the furred variety...bacterial pink eye can be very, very contagious. I've seen it spread through a horse barn just by somebody petting an infected horse and then petting other horses in the barn. Fortunately, it's easily treated.