Thank you Wolf for your help!
I tried that but had much difficulties. I'll explain in a little more details what I do, so maybe you can tell me what I'm doing wrong.
I'm training her on a perch. I attached a small bowl to one end of the perch, filled with treats (seeds). I keep the bowl covered at all times except when I want her to have access to the treats.
When she sees me taking the harness out of the drawer, she flies to the perch and wait there. I present the collar loop between her head and the treat bowl, and I uncover the bowl. She puts her head through the collar to get a seed from the bowl. Then, one of the following two scenarios occurs:
1) Most of the time: after grabbing a seed she immediately pulls her head out of the collar and walks a couple steps back and eats. If I follow her with the harness so that the collar stays on her as she walks back, she gets very irritated and bites the harness and shakes her head instead of eating the treat. In this case I remove the collar and close the treat bowl and let her eat the seed she already got and calm down.
2) Rarely: sometimes she doesn't walk away and instead she stays near the bowl to eat her seed without trying to pull her head out of the collar. In this (rare and precious) case I let her eat as many seeds as she wants while she has the collar on and doesn't seem disturbed by it. But as soon as she shows that she wants to get out of the collar, I immediately remove it and close the seed bowl at the same time.
I've tried to put the whole harness on her when that second scenario occurred, and was able to do it a couple times (but that is extremely rare, and doesn't seem to occur more and more often with time). When that happened, I let her eat as much as she wanted, then removed the harness (and the free access to the treats) as soon as she apparently became uncomfortable.
I agree that it would be better to not let her have treats until the harness is fully on her, so she would be rewarded for letting me put it fully on her. The problem is, I can only do it if she is very busy eating. Actually she will put her head through the collar only if she can see seeds on the other side of the loop. (Maybe I need to work on that as a priority, and get her to put her head through the loop without luring her with the seeds?)
In any case, she is clearly not afraid of the harness because she puts her head voluntarily very easily when she wants to.
Let me know if my explanations don't make sense
Thanks again for your help.