Property tests are nice for lots of things, but for an AST parser? You'd basically have to re-implement the parser in order to test the parser, wouldn't you?
I suppose you could test "if I convert the AST back to a string do I get the same result", but that's not actually your goal with an Abstract Syntax Tree. If nothing else the white space should be allowed to change.
What sort of property tests did you have in mind?