If I am making an egg pasta, can I substitute quinoa flour for wheat flour (semolina, durum, all purpose, etc)? Or will the presence of the eggs not be enough to offset the absence of gluten, and I would need to add another binder (I am thinking xanthum gum or potato starch)?
I have never tried making pasta with just quinoa flour, but use a mix of potato starch and corn flour. So my pasta contains a lot of starch.
The issue is that the pasta gets really short and need to be handled quite carefully after rolling it. I have used it to make tagliatelle, ravioli, spaghetti, lasagna and tortellini with great success (my comparison is store bought pasta, not normal pasta as I haven't eaten that in 10 years when I found out I was allergic).
I don't really have a recipe, as I never follow them. But for one person I add two egg yolks, one whole egg, ~1 tablespoon of olive oil and some random mix of the flour until it feels smooth and nice to work with. I have found the resting time of this pasta to be essential, and I always allow it to rest for at least 20 minutes.
The eggs in standard egg pasta are not enough to hold it together if made with gluten free flour. Maybe you can do it if you keep increasing the egg ratio, but it's hard to say how far you can go before ending up with something closer to pancake batter than to pasta dough.
Adding a binder should help, but I'm not certain what you can use as a binder. Neither xanthan gum nor potato starch are binders, they are both thickeners. The xanthan does give you a snotty gel, but not a truly cohesive structure the way you get with gluten.
Still, lacking a true protein based binder option, one of the snotty thickeners might be a good choice. Psyllum or chia are probably better than xanthan. They will help somewhat against crumbling, but also the thickening they contribute will allow you to use more egg, which will do the real binding work.
Another option is to start making spätzle instead of traditional Italian pasta. You will have less problems with handling a not-quite-cohesive spätzle batter than with trying to knead and roll gluten free tagliatelle or other similar shapes.
You could also try looking at molecular gastronomy recipes for pseudo noodles made from vegetable juice and a gelling agent, and see if you can adapt them by incorporating some quinoa into the liquid. But this goes quite far from your original intent, and will be noodlelike in shape only, without much resemblance in taste and texture. It will also be predominantly juice based, with little quinoa and no egg.