If your venue gives you permission and the Wedding Minister/Officiant is fine with it, then yes of course bring Fido or Lulu along.
Many couples believe that their beloved pet is truly a part of their family and therefore it should be included in the photographs which mark their huge event. I actually love it when the couple brings along their dog or doggies to the ceremony. It never fails to bring a smile to everyone’s face, especially the couple.
So, if the venue is in agreeance, I say do it. However, you must have a "handler" to look after your pet throughout the day and evening. You won't want to be looking after your dog because you'll have way too much to do, and too many people to acknowledge and spend time with. Therefore, a dog handler should be designated for the day.
And don’t forget to adorn your pet with some wedding attire, such as a bow tie or a white bandana. Even a little tulle skirt if you want her to be a fashionista and fit in with the bridal party. And don't forget the dog’s leash, it can be adorned with vine leaves or flowers as it walks down the aisle.