Disclaimer: Have not read all the responses. Credentials: 12+ years as a Vet Tech and now a Physical Therapist.
To answer your leash question: I have run holding a leash, with a regular leash around my waist, and now with a 'shock cord' type leash. By far my favorite is the last. Something similar to this (as a side note - Chewy.com is amazing):
https://www.chewy.com/...WZ-KzGRoC9oAQAvD_BwE I like this for several reasons. Even a well trained dog can find something suddenly interesting and want to try to go for it. This leash absorbs that shock and prevents you from being pulled off your feet. Also running hands free is much better for your form long term - which can prevent injury. Please whatever you do, never use a flexi-lead.
So much of when it is actually safe to run distance, terrain, etc with your dog depends on breed. I have a 50# dog that reached skeletal maturity at about 10 months. Prior to skeletal maturity (likely 10 months - 18 months) you want to be cautious with 'long' runs. Slowly increasing for her is going to be important regardless of age. Also, your decision to spay and at what age (assuming the dog is not already) can also play into this. Dogs that are left unaltered for at least 1 year have significantly fewer orthopedic injuries than dogs that are 'fixed' early in life. Females also have fewer issues with urinary leakage later in life as well as hormonal and autoimmune diseases. This is by FAR a more significant factor than running at a young age. Also ensuring that the pup is getting adequate protein and nutrition is important. High quality feed is a must if you want an athlete dog. We also have used Iceland Pure omega-3 fatty acids to keep our dogs' joints feeling good. Finally, if you are motivated and want to deal with it - allowing her to go through at least one heat cycle can decrease the risk of some cancers, the dog version of ACL injury, and several other common complaints. We elected to have our dog's uterus removed, but not her ovaries. So she style 'cycles' 2x/year, but can't have puppies. This takes patience and is NOT for everyone, but can be a good alternative. (for the male dog owners - vasectomies exist).
Finally, you will find training advice all over. Positive training is super hot and popular. Other tools used correctly (choke, pinch, e-collars) can be really helpful and be used in NON-abusive ways. Our female is a Kelpie. A high drive Australian herding breed. Our herding trainer had an interesting comment. Do you want your dog to work for payment (treats) or to please you? Now Kelpie's and other highly biddable dogs WANT to please us, so the best method for training her for good leash manners I have found (in 4 years) is the herding trainers suggestion. if she starts to pull, just jiggle the leash. You don't have to yank, yell, or be mean...just make it annoying. The dog stops, you stop. In 2 runs we were having a much better time. Harnesses, gentle leaders, etc - all alter the dog's gait. If you are running distance - their form is as important as your form. Learn how your dog needs to learn and take the time to train.
OK - getting off my soap box.
Good luck and enjoy the pup!
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