As a former QA manager of a successful software company, I'd say grow it as soon as you release your first program. (Before, if possible). Really, as soon as you can afford it. But, as a developer, you should be doing a lot of the testing yourself during the entire dev cycle, not just at the end. QA's job (depending on which book you read) is to handle a lot of legacy testing, SMOKE testing, regression testing, real-world testing, and writing automated test procedures, processes and plans, etc.
Ad hoc testing is only a small part of what QA should be doing. There are two major areas of focus for QA. 1) Does the software DO what it is supposed to do, and meet the requirements in a way that is usable by the customer, and 2) Does the software NOT do what it's NOT supposed to do.
Planed, procedural and Ad hoc testing are the basis of QA. I've found that if you only do one type of testing or the other, you will not have a successful QA cycle.
I've released software without QA when working on my own, but I can tell you, it is ALWAYS more error prone, no matter how much I test it. A second+ set of eyes is the best thing for software.
Just make sure you build your team out of A.D.D. anal-retentive, computer geeks. You'll get your best results that way. :) People who are PROUD when they can make someones software go BOOM... heh.. (Just kidding.. I know a lot of QA Testers who do not have A.D.D)...