Is it okay to bring my dog to the crag?
It depends on the crag and it depends on your dog.
If you're climbing in a National Park, you basically have you leave your pet at home. With a few exceptions, dogs basically aren't permitted beyond the parking lots.
If you're climbing elsewhere, check the local regulations before you head out.
It's common for state parks to allow dogs only on a controlled leash, which technically means you can't tie your dog up to a tree and start climbing. Many fines have been issued in such cases, particularly at popular sport crags.
If you do have a well-behaved dog and you decide to bring it, please keep Fido under control and pick up its waste.
If a non-climber has a bad encounter with your pet, it's likely they'll complain to the park administration which will jeopardize climbing access. Don't be the guy or girl that ruins it for everyone.
Your freedom to enjoy the outdoors with your pet is a right limited by everyone else's right to safety and tranquility.