A lot of babies go through a big growth spurt at 10 months, so they tend to seem a little "behind" at the 9 month appointment. They are not technically behind, it's just that they haven't had the big jump in growth yet. And your doctor is correct that weight gain starts to slow down once they become very active. It sounds like she's eating plenty and getting proper nutrition. I wouldn't worry so much.
I agree. There is a 9m growth spurt and sometimes it happens closer to 10m so it just depends on the timing of your appointment and activity level of the baby. If she drops more at 12m then it's a concern but if she stays at the new curve it's ok.
ETA - I was in the same situation as you OP with my DS and he ended up fine.