Well, I admit I had to Google the word, as I'd never encountered it in English (53-year-old native speaker), and was surprised to find it did exist, but seems to be defined as "oily" or "greasy", rather than "fat" (as in "obese"). So I suppose it's just about possible, if you were talking about peacock as meat, on the plate. And I accept peacock can be and has been eaten, in other times than ours. So possibly it's OK, but not to describe the living bird.
I too am a native English speaker (aged 62) and also hadn't come across "pinguid", so thanks to David for teaching me a new word.
I have a vague memory from studying Roman Civilisation at school that peacock was quite a popular dish. So, following on from Tina's thoughts, whether to use fat or pinguid probably depends on if you are selecting a bird in the forum or eating it. Without context, we just can't tell, so either should be OK.