If it's an active stand of alfalfa, it will only be used to control winter annuals before the alfalfa breaks dormancy in the spring. Not sure when you are hunting but where I'm at, bird season would be long gone by spray time. Also, the re-entry interval is only 24 hours after application. if it had been sprayed very recently and the dogs ate a bunch of foliage I guess it could be a problem.
Paraquat has been around since the 60's. Used and stored properly its a great herbicide. Not dangerous at all, again, used properly.