Is it worth upgrading?
As you can audition the Chord, it's a question that you (and only you) will soon be able to answer.
I've tried a few DACs up to around £600 and, like many other people, have found sound quality differences to be subtle at best.
A quick look shows the Qutest to be around 40x the cost of your Fiio!
It would be really interesting for you to get a dealer (or someone with you at home) to play the same track(s) switching between the Chord and your Fiio, without you knowing which you're listening to.
There could be no better way of answering your question.
I see the Yamaha is a CD player as well, but both would give you the useful USB input option, for direct connection to your PC - something you'd also get with much cheaper DACs of course.
I'm quite interested in the Kahdas tone board, I'm not saying you should be, not least because you'd really need to put it in an enclosure, but, in terms of performance, I think it could be all that's required.
I own a little £100 DAC , it's in an enclosure (not unlike your Fiio), nothing much to look at and out of sight anyway - it's the sound that counts.
This video is under 10 minutes long so might be worth a look.
OK, it's not the Qutest and it's only one man's opinions, but I think it nicely illustrates the subtle differences between vastly different price points.
View: https://www.youtube.com/watch?v=Kj7NQ5EPzls