"As if I would talk on such a subject!" meaning.
This sentence is from "Alice in wonderland". I brought the original phrase below.

`We won't talk about her any more if you'd rather not.'
`We indeed!' cried the Mouse, who was trembling down to the end
of his tail. `As if I would talk on such a subject! Our family
always HATED cats: nasty, low, vulgar things! Don't let me hear
the name again!'

I'm given to understand that the word 'as if' is used like "I felt as if I were floating in the air".
So the question is what is the meaning of "As if I would talk on such a subject!"?

Question

"As if I would talk on such a subject!" meaning.
This sentence is from "Alice in wonderland". I brought the original phrase below.

`We won't talk about her any more if you'd rather not.'
`We indeed!' cried the Mouse, who was trembling down to the end
of his tail.  `As if I would talk on such a subject!  Our family
always HATED cats:  nasty, low, vulgar things!  Don't let me hear
the name again!'

I'm given to understand that the word 'as if' is used like "I felt as if I were floating in the air".
So the question is what is the meaning of "As if I would talk on such a subject!"?

Answer

I would like to add to Neil's answer that it's a bit stronger than simple would not.

"As if I would talk on such a subject"  gives the idea of
"it would be ridiculous to think I would talk about such a subject"

Another example: 
Person A: "I can't wait to go to college."
Person B: "As if you are going to graduate high school."

Meaning: It would be ridiculous to think you would go to college because you are not even going to pass high school.

Answer

It means "I would not talk about such a subject". 'As if I would' is an expression that means 'I would not'