I guess I got lucky. Used the DAV folks on base as well, but didn't file my claim until 3 months after my DOS (several reasons - didn't want to inadvertently force a DNIF, and wasn't sure of post-separation job plans) . It was filed as a fully-developed claim (this is also important). FIVE WEEKS after the fully-developed claim was submitted I went in for the exam. Three weeks after that I got my rating and my first payment, including back pay back to my DOS.
EIGHT WEEKS from filing to seeing $$. Southern AZ (Tucson) VA rocks, btw. I've heard anecdotal stories of multi-year waits in other locales, and so the VA you choose to do the filing at is VERY important. If you don't mind a trip or two to Tucson, I'd highly recommend filing your claim there.