There isn’t a formal OTQH group like there is for TBs (although some of the TB groups do list QHs sometimes). In general, I think QHs tend to be in high demand as barrel racing or roping or match racing prospects, so they’re not as hard to place - it’s pretty common for a 5yo gelding to fetch $3,500-7,500 straight off the track. There are a few FB groups that list horses for sale, but there are also many owners and trainers who very much love their horses and want to find the best place for them when they’re done running, so making some private connections might be the way to go.
If you’re in Michigan, the meet at Indiana Grand is going on right now, but wraps up in late October - you might try calling the QH Racing Association of Indiana and see if they know of people wanting to sell some runners when that finishes. They also have their sale on September 15, so that might be worth attending. They’re also now racing at Prairie Meadows (Iowa) so keep an eye on that meet, as well.
I have trained and worked with OTQHs. After you let them down, they’re just like any other horse/QH - most are very easy going. Some can have quirks. Just like any racehorse, they don’t really know leg cues, they have to relearn all that. Also if you smootch real loudly to them when they’re standing still, they tend to launch forward, so hang on first. lol