Hi J.,
My son was very afraid of the tables as well. Once he hit about 6 months old, he really started getting scared and would cry the whole time. I think it was because they don't feel too sturdy, they kind of sink with a kid on them - that may be transferrence though, I know I wouldn't want to be on one!
Anyway, I just got very good at changing him either (1) standing up or (2) laying down in either his stroller or in the large part of a shopping cart (just put down something to make the shopping cart feel a little softer, even a shirt will do, and then lay her down just like a changing table).
He never grew out of it, but it really wasn't a problem once I came up with alternatives. So, I would say to trust your little ones instincts that the changing table is not for her and then plan out a couple different options based on the "kind of diaper" she has :) No need for diaper changing to be tramautic in public, for either of you!!!
Good luck!