I can't imagine that the tip of a brush as small and soft as we use produces a perfect dot, maybe a micro pen is your best bet. When I do paint a dot though I'm using very watered down paint loaded on the very tip like a bead and I place it directly on like a stab more than a stroke, are you doing that? Ps I am no master
I think I've heard of people using a pin or toothpick to do dots easier than using a brush. The rigidity means it doesn't flex when it hits the surface.
wn7 size1 is my favourite for infinity. i paint very detailed faces with it including colored eyes (well avicenna is not the best example as she has dark brown eyes but you get the picture that the brush is not limiting me).
I use a whole mixed bag. W&N Series 7s, my first one lasted a decade before I finally retired it to basecoats only. I have a #3, #1, and I think a #00. I can paint eyebrows with my OLD #3. Tamiya bamboo brushes. both middle 中 and small 小 (looks like I need to install the Asian character entry in this machine...) I keep some GW drybrushes around for drybrushing, as well as a couple really big flat brushes. Also have some P3, Vallejo, and a whole crapton of others. Even have some old Floquil 10/0 Liner brushes (which have super-long bristles). Also have a long-bristled Signwriter's brush that I use for washes and big work like banners. I also use micron pens for some effects.
As others said W&N Series 7 #1 can cover almost all your needs in painting infinity miniatures. Bought mine year ago and it's still in perfect shape. Also have #000 but IMO it's too small and cant hold enough water leading to very fast drying of paint on a tip. Before it I've used Da Vinci Restauro #1 and it's somewhat same quality, but have more narrow shape making its nice for lining, freehands end etc. but not that good for blends and large surfaces.
The dot is a 2 step process with brushes. Step one is of course painting the white or black, which as noted is more oval than round. Step two is painting over a portion of that oval to leave a dot. It is tedious, but it works well for things like the white dot to highlight eyes. See the image below: Use magnification, steady your hands, and don't try to adjust it too much, if at all, after you've done it. Especially after seeing it under extreme magnification that the dots are a bit off (as above). A sharpened toothpick or bamboo skewer can work, but is hard to control and the paint on it dries quickly. I've never used a micropen for eyes. I think I'll get some and experiment. Cheap natural bristle brushes work for quite a bit of what you may want to do. Golden Taklon brushes will be fine too, for a very limited time. They curl and fray quickly. For blocking in colors or brush priming they serve well enough. The emphasis here is on cheap. Even the expensive synthetics curl and fray, and do so almost as quickly as the cheap ones. Using these sorts of brushes will let you keep the good brushes in usable shape for a longer period of time, since you only use them when it really matters. Currently Using: #3/0 Imex sable, #0 W&N series 7, #1W&N series 7 (the workhorse), #2 Raphael 8404 (another workhorse). And a whole lot of cheap brushes for things like terrain and priming and base coating. An interesting way to check the tip of your brush is to get it wet, and make sure no air is trapped by the bristles -- thing which happens with sable brushes-- then treat it like a drum stick and rap it once or twice against the side of your water cup or other hard service so that the lower part of the ferrule strikes the edge of the cup. A good brush immediately points up when you do this. Saves on licking (thing never to do) or wiping the brush to get a point. Wiping the brush sometimes picks up tiny hairs or lint.
To the usual suspects (s7, 840x) already mentioned, add Escoda 1212. As for eyes, or any other thing, sometimes the trick is to do in steps that cover the errors of the previous, allowing approximate steps instead of perfect "direct". http://archive.li/Icvjz here you can see how the blue goes over the brown and later that is fixed (I prefer skin after pupil/iris).