So here's what I did for our Q1000. First, remove the bracket holding the regulator, and the regulator itself:
...Revealing the 1/8" NPT male threaded fitting:
Next, buy some parts. From left to right: 1/4" NPT brass elbow (personal preference, a straight coupler works too!), 1/8" NPT to 1/4" NPT brass bushing, Camco #59903 brass quick-connect fitting, and Camco #57282 quick connect hose:
Put it all together. I couldn't find any yellow teflon tape, so I used the white stuff.
I turned it all on and tested for leaks. There were none so I fired up the grill, and it seems to be working okay. Like I said, use of the elbow is personal preference. A straight 1/4" coupler would work just fine too. The big expense was the hose, since the brass fittings were only a few bucks each. I hope this helps someone who might be wondering how to do this themselves. Thanks for the advice everyone.