I currently own an SQ5. I’m a solo singer and run my music from an iPad. I’m considering switching to a smaller mixer, specifically the CQ. My main concern is vocal quality—can I still get a great vocal sound, or is the overall quality significantly lower due to the price difference? Are the preamps, effects, and overall sound good enough for professional vocal mixing, or will I notice a big downgrade compared to the SQ5?
I have both. I do not experience a big difference in sound quality. Biggest differences on cq are: no expansion, no faders, routing nor patching & simpler fx settings. But still usable fx imho. A CQ12 would fit your needs. I use it all the time for small gigs. One caveat: it’s not convenient to use the same iPad for controlling the cq and streaming music to the cq because everytime you leave the cq mixpad app to start-stop music the mixpad Connection to the cq is lost and you have to reconnect when you switch to mixpad again. Not a cq bug but an IOS Safety precaution. Better to stream music from your phone and use the iPad for the mixpad app.
Oh ik zie nu pas dat ik ook in het Nederlands had kunnen antwoorden 
Je kunt de cq12 ook op een statief naast je zetten en via het touch screen bedienen en de iPad voor de muziek gebruiken.
I found the CQ20b a better tool for the aplication you have described. I actually sold my SQ5 when the 20b worked so well for my solo shows. The SD card protocol is far surperior for BU tracks than the SQs options and two of the soft buttons can be set for easy start stop controls. My new LV1 Classic console replaced the SQ5.
Hugh
In a live production environment
there are so many other factors that will affect sound more than mic preamps.
The CQ would be much easier to use for solo acts.