Your pup is only 11 months. Things can and do change as they reach maturity. Just because other people do it and nothing bad has happened yet does not mean it's a wise decision. There have been countless instances of things going wrong that have been posted here on DT. Usually the dobe is not at fault but like 4x4 mentioned this is a breed that is determined to stand up for itself to protect its owner in a situation like that. In that scenario it can get very ugly.
Along with what 4x4 has brought up dobermans are prone to same sex aggression. This is something that does not present itself generally until the dog is mature. Everything can be going fine and in the blink of an eye it's not, and breaking up a fight involving one or more determined large breed dogs can be very difficult. I've been there, having broke up a fight between my male and another male doberman. I broke a finger in the process. Not fun!
Dobermans are also not a social breed. They were not bred to get along with or work alongside other dogs like say the hound breeds. They were bred as personal protectors, to work closely with one handler, thus, same sex aggression and dog aggression are byproducts of their breeding. If you read the doberman standard aggression is described to some degree as inherent for the breed. It's important to acknowledge this so you don't expect your dog to be something she's not.
A better place to burn off energy with your doberman is a secluded field, ball field, hiking trails, biking with your dog (18+ months only), or training for agility, dock diving, flyball etc. Play dates with dogs you know and capable owners are also a better option.
Greenkouki and 4x4 bring up some very valid points. My girl was and is a rough and tumble, high prey drive sort of girl.
I took her to the dog park regularly, but definitely noticed a change in her as she matured.
She was less tolerant of other dogs that did not pick up the signals she was giving out about wanting to rest awhile.
Greenkouki is right on point in saying that things can happen in the blink of an eye.
The park I took my girl to was nowhere near as big as the one you describe, but even a dog minding their own business can get attacked. It happened to my girl. She was attacked by a bulldog that did not like other dogs. For no reason that I could see, this bulldog attacked Jazzy from behind from about 30 feet away. The bulldog was a female.
Jazzy whipped around and met the attack head on. My being close to her and her having a harness with a strap type handle, stopped the situation from being much worse. I was able to grab her and pretty much snatch my snarling, Cujo girl away. It was all I could do to hold onto her, put on her leash, while keeping my body between her and the bulldog. Thankfully, the bulldog didn't try to continue the attack as I could have been bitten. The stupid owner did nothing.
My girl is good with most dogs and most people, but she will not back down. She is particularly less tolerant of other females.
My girl has been attacked 4 times in the almost 5 years I have had her. Twice in the park. Once by a pitbull female at PetSmart and once in my own fenced yard. The Neighbor's dog who is dog and people reactive got loose and attacked her under the fence. Jazzy got bitten on the foot.
I have been lucky that these 4 instances did not make her fearful of other dogs. I know through friends of friends whose dogs were forever changed by one attack.
I have heard many times the saying, something along the the lines of, everything was fine until it wasn't. The bulldog attack on my girl was the last time she ever went to the park.
From what you say, you are doing the right things by not going during peak hours etc. I pray that everything goes well and you never have an incident where your sweet girl gets hurt.
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