I dont know if you clicker train, but what our trainer had us do at first was click and treat for looking at a strange dog (even if super far away), then click and treat for approaching each step etc, keep treating every time she sees the other dog. Then they sort of start to associate the other dogs with a really fun, good thing. Our puppy would growl and bark and hide at other dogs when she was 10 weeks old (it was a mini class offered by my vet where all dogs had shots) but now at 12 weeks she loves seeing other dogs, it makes her really happy and she always wants to greet them because it equals good treats
It sounds like youre doing a good job though. I wouldn't rub her and reassure her when she whines though, it increases it. If she whines, just walk away father until she quits and act like there's no big deal going on and she will get the hint that her behavior is unnecessary since you are so calm.
I would try to get into puppy class earlier if any way possible!