If you have mild periodontitis with a SMALL amount of bone loss, is it still possible to get orthodontic treatment such as braces or is it dangerous?

Yes, you can. In many cases orthodontics can help reduce the symptoms of periodontal disease. Orthodontist should evaluate the periodontal tissues prior to beginning orthodontic treatment, and periodically update the evaluation throughout orthodontic treatment.
Team approach. Before doing Orthodontic treatment all infections (cavities, abscesses, gum disease) must be fully under control. You need a team composed of AT LEAST your General Dentist, an Orthodontic Specialist, and a Periodontist. See an Orthodontist to get the ball rolling.