The trouble here is that cinema is a completely different medium, and what works well in a book (or a radio dramatisation) doesn't always do likewise in a movie. Maybe PJ & co just wanted to get in some of the information about dwarf women from the appendices? A laudable objective, and it serves to round off the species, make them seem more real. In all honesty, the interplay between Gimli and Eowyn in that particular scene is very good, and does serve as a moment of light-hearted relief before the heavy stuff comes crashing down. The pratfall is regrettable, but it does create a genuine dramatic contrast with what happens just after it.
It has to be admitted that Gimli gets one of the best scenes in the entire trilogy too - the "never thought I'd die fighting side by side with an Elf" scene. Beautiful stuff, and I can forgive a lot of crimes for that.