Accepted answer
At 20 mg/mL a 1 mg dose is 0.05 mL — 5 units on a U-100 barrel — and no needle gauge changes that number. Gauge changes three other things: how long the draw takes, how much stays behind in the hub, and how much rubber you core out of the stopper. On the 18G scale a larger number is a finer needle, so an 18G drawing needle is coarse enough to draw quickly and coarse enough to cut a visible plug from the stopper. If you are drawing 5 units at a time, the dead space matters more than the bore: a fixed-needle barrel loses microlitres, a luer hub loses tens of them, and at 20 mg/mL each microlitre is 20 µg.
The short version: 21G to 23G to draw, 29G to 31G to inject, and never the same needle for both.
Flow through a needle scales with the fourth power of the internal radius under the Hagen–Poiseuille relation. Halving the radius reduces flow sixteen-fold at the same pressure, which is why a 31G needle draws so much more slowly than a 21G.
To be exact about it, stopper coring — punching a disc of rubber into the solution — is a large-bore phenomenon. An 18G or 21G needle inserted straight and fast is the classic way to do it; inserting at a slight angle with the bevel up reduces the risk.
The Hagen–Poiseuille relation gives flow proportional to the fourth power of radius, which is the quantitative basis for every gauge recommendation here.
Flow goes as the fourth power of radius. That is why the difference feels so large.