Is it possible to create a single queue and send failover to different places depending on how the queue was called?
For example, I want the (dynamic) queue to ring and if no answer send the person to the main IVR menu.
I also want to use the same dynamic queue if someone presses 0 (for operator) and send the user to a voicemail box if there is no answer.
Any idea how I might do this?
not really today, but there is a commercial module that is being developed in the works that will be able to create ‘virtual’ queues out of a single queue.
What that means is several of the queue options will be able to be changed in the call flow prior to hitting the real queue and those changes will override the main queue settings. Destination if no answer is one of those settings that can be changed and many of the other ones as well.
It will be targeted for 2.11 and is not too far off from being done.
There must be a way to do it “today”. You work for FreePBX spill the beans 
I need a solution by the 20th, not one or more months away.
“not really today” usually means not with anything standard.
There’s almost always a way to achieve what you want in FreePBX.
You can send the destination to some custom dialplan by registering a new destination in the destination registry, and then from there determine which way the call came in from your two sources. Figuring that out may take some creativity, it really depends on your specific configuration and depending on that, see if anything needs to be ‘added’ to the call flow or not to better identify the call.
So … yes there’s a way to do it today, but it will take some work and custom dialplan to do it. The module, when finished, will be able to directly configure it.
Lastly, if you put in on the 2.11 beta, the necessary code is in place in the queues module to support this functionality but you would still have to write in some custom dialplan before hitting the module to set an appropriate channel variable to enable the ability.
Good luck, sorry we are a few weeks too late for you.