And this article from a dog trainer, on whether it is safe to jog with a dog (cavaliers are both a toy breed and brachycephalic):
Before You Start Your Dog’s Exercise Program
Check with your dog’s veterinarian before starting an exercise program. He or she can check your dog for any health issues that may be aggravated by exercise and suggest safe activities. Some size, breed and age considerations are:
*Breeds with short or flat noses (brachycephalic breeds) can have trouble breathing when exercised vigorously, especially in warmer climates.
*Exercise is great for energetic young dogs, but sustained jogging or running is not recommended for young dogs (under 18 months) whose bones haven’t finished growing.
Also see this AKC research article on the issue:
What breed is your dog? If you have a medium or large sporting breed or one of the medium or large herding, working or hound breeds, then it’s likely that your dog will have no trouble keeping up with you as you jog. Some of these breeds may have a high energy level, such as the Border Collie, while other breeds may have been bred to run, such as the Greyhound and the Whippet. These dogs will probably love going jogging with you. However, if you have a toy dog or a smaller breed, one of the dwarf breeds or a brachycephalic breed (short-muzzled), then jogging is not a good idea.