Yes, that's what was shown, but I consider that scene chronologically incorrect (in other words, it actually happened later than it apparently did). Ducky appears to have hardly grown at all since she hatched, while Littlefoot, Cera, and Ruby have had a lot of time to grow to their current sizes. For them to have that much time, they must be older than Ducky.
You probably might say that Spike's size and age would contradict each other in this case. Yes, that might be true, but when Ducky pulled him out of his egg, he was already bigger than her. Anyway, I'm sure other people have already talked about Spike's rapid early growth, so I'll just ignore it for now.