While your dog can be one of the best ice breakers to start a conversation with anyone, brining it on a date is usually a mistake. No matter how cute your dog is, bringing it to a (first) date with someone you hardly know will necessarily be a distraction, and you will not be able to give your full and undivided attention to whoever it is you meet. This is true even if your date loves dogs. No matter how wonderful your dog is, it is very likely to be a third wheel on your date, just like if you brought a friend along on your date. It will turn a good date into not so good, and an ok date to a mediocre encounter. Your first date should be a one-on-one interaction. Bringing a dog on that date is almost as bad as bringing a friend. If you have no one to leave your dog with when going out, then wait till you can make that arrangement.
You may also be on the other end of this. What if you find yourself on a date with someone who you kind of like but you can’t quite get all of their attention because of the dog yanking their hand or just running around while you are trying to talk? This will prevent you from focusing on each other and getting to know each other. The direct yet polite way to deal with this type of situation is to address it, but not right then and there, but rather later. Tell that guy or a girl when you set up your next date, maybe the date after, that you really look forward to your next date, but you would really appreciate having them all to yourself the next time you see them, without having to compete over them with their dog.