Based on the bug/thread it would appear there are some ambiguity problems with supporting a dotted property accessor. Based on the mailing list thread it would seem that evaluating the queryField string would be your best bet:
def result = [a: [b: [c: 42]]]
def queryString = 'a.b.c'
def evalResult = Eval.x(result, 'x.' + queryString)
assert evalResult == 42
Script on Groovy Web Console
The mailing list thread is a little old, so there's a new-ish (since at least 1.7.2) Eval class that can help out with running small snippets that don't have a large binding.
Otherwise, you can split the string and recursively do property evaluations on the object, effectively reproducing a subset of GPath traversal behavior.