Your probelm is not with QA, in fact, if your QA is doing Testing, the delays are pretty much the least of your worries. Please let me expalin (again, as it's common misconception in the Programming industry)... QA Assures the quality of the product by overseeing the entire SDLC, from Requirements (maybe earlier), through development, verification, release and support. Testing ensures that no obvious defects exist in the code. There is a very large and important difference. If you had true QA, they would be all over the Test/ V&V department asking why they were costing the business time (and therefore money) delaying releases, or all over project managment ensusring they were managing project scheduling properly, or all over managment making sure there were enough testers for the code being produced etc...
So assumeing by QA you really mean Test, back to the orginal question. Code Complete got it right - the cost of a defect is the time taken from insertion to correction. Early detection is only useful if you also correct it early, but most peoples interpretation is wrong.
(Note : I am playing Devils advocate here, don't take any of this to literally as I know nothing of you situation)
The delay cause by your Test department is a cost, absolutely, however, I have to ask, if you are waiting for them to find your defects, what are you doing - should you not be finding you own defects? Perhaps if they had less work (through higher quality input with less defects from you), the delay would not be as significant and the cost less - as a manager I would ask you how you plan to reduce the defects in the code you deliver to test, as (based on your argument) those defects cost more if found by test then yourself.
Also as you manager, I might state that is not Tests job find your defects, Their job is to find there are no defects - if you are expecting them to find defects, maybe you have not done your job well enough.
Be careful how you approach this. If you dont have a solution to the problem, you are likely to come off second best.