動物 (doubutsu) - all moving things?

Does the word 動物 mean all creatures i.e. crustaceans, bugs and fish and (more importantly) would this commonly understood as such? It's translation is animal and the kanji means moving things but in English some people make a distinction between animals and bugs/shrimp etc.

I ask because I'm trying to figure out the best way to say I'm vegetarian. Saying I don't eat 肉 and 魚 doesn't work because I've been offered shrimp. Next I want to try saying doubutsu tabemasen or maybe ikimono tabemasen to see if that's better understood.