(I'm doing these slightly out of order for reasons of convenience)
My dogs was pooped out.
"Dogs" was slang for "feet", originally from journalist T. A. Dorgan in 1913. "Pooped out" is an idiom meaning that someone/something is exhausted. Thus "My dogs was pooped out" is an informal way of saying "My feet are very tired".
He wasn't puttin' on no dog.
"Put on the dog" is an idiom meaning to to behave self-importantly/ostentatiously. Thus, "He wasn't puttin' on no dog" would mean "He wasn't acting self-important".
He just done it for ducks.
This one is trickier. I found a forum thread speculating on the same line, and they weren't sure:
From the context, it seems to mean that he just did it for a joke, or for fun. I can't recall having heard this expression before.
I can't find any other instance of its use, but I suspect Barque [the previous poster] is correct. Note that "ducks" rhymes with "yucks," which is slang for laughs.
The context from the book:
"Well, it makes you mad to hear a guy use big words. 'Course with a preacher it's all right because nobody would fool around with a preacher anyway. But this guy was funny. You didn't give a damn when he said a big word 'cause he just done it for ducks. He wasn't puttin' on no dog."
"Well, it makes you upset when someone uses big, fancy words. Of course it's okay with a preacher, because no one would dare mess with a preacher anyways. But this guy was funny. You didn't care when he used big, fancy words because he <just done it for ducks>. He wasn't acting self-important."
So yes, it makes sense in context that "just done it for ducks" would mean "just did it for fun".
(The most relevant duck-related idiom I found was in another forum post, which said that "just for ducks" meant "just for the hell of it" - but no one else knew it, and the post said it was from the 1970s which doesn't fit the timeline here.)