I apologize that no one has responded to your question sooner. Different experts come online at various times. I just came online and saw your question. I'm sorry to hear your goldfish isn't doing well. What you have planned with the second bowl for continued treatment is fine. The sooner you can do it, the better, but wait until the water in the second bowl is the same temperature as that in the bowl Pebbles is now in. A sudden temperature change is bad for her. The fin rot may not heal until you have her in a bigger tank. Poor water quality makes it nearly impossible to cure such illnesses, and small bowls almost always have poor water quality.
Goldfish can change colors, but black on the areas you mentioned is often a sign of ammonia toxicity. The ammonia causes damage resulting in red streaks, and as the damage heals, it becomes black. It may or may not change as time passes. Goldfish need to have ammonia at zero, and in a bowl, it is nearly impossible to keep it that low.
A tank is an excellent idea, but make sure it's big enough. Goldfish produce a tremendous amount of waste, and your tank has probably not been able to cycle properly because of that. It used to be recommended to have about 4 liters of water per inch of fish. That still holds true for tropical fish, but not for goldfish. I find they do best with about 100 liters per fish, regardless of size. I’ll share my own experience with 12 inches total of goldfish (3 fish). They are in a 90 gallon (about 340 liters) tank. I have an undergravel filter, a hanging filter, and a powerful canister filter. It takes all three of those filters to maintain perfect water quality. Regardless of tank size, frequent water testing and changing is needed. Goldfish tank size is an area where pet store personnel often give out incorrect information. They may not know, or they may simply want to sell more fish.
If you get a bigger tank, you'll need to cycle the tank before putting Pebbles in. If you skip that step, you'll just have more trouble. We now usually cycle tanks without fish. There are other ways to cycle a tank. The following website gives detailed instructions and also explains cycling in depth.http://animal-world.com/encyclo/fresh/information/CycleAquarium.php
If you have more questions, let me know by clicking on REPLY. I hope you'll be able to quickly return Pebbles to health.