Your dog will be discriminated against. It is not that a doberman (or any of the other "dangerous" breeds) is more likely to bite, it is when they do they can cause severe physical damage. And no one can say for a fact that any particular dog will not bite under the right circumstances. How often after any dog bite has the owner said "he/she has never done that before". And because of that many people will fear them, or at least be very leery of being around them.
A park's insurance carrier will likely prohibit them. And just as likely, a park owner will not want them there due to the discomfort of many people to them. A park that routinely lets those breeds in will likely lose future customers. An unfortunate fact of life.