Thank you for taking her in - poor dear, glad to hear she's got a new forever home! I think Daisy has the right of it, go slow and build trust with her. Since she's been in so many different places, I would say go very slow with her, let her explore her cage on her own, but mostly leave her to herself if that makes sense. In my experience, a bird won't really feel comfortable in their environment, with their people, etc if they don't first feel safe in their cage. I think a lot can be said for them having a safe space all to themselves to retreat to in a moment of stress or fear. Give her time, go slow, and try your best to make sure every interaction you have with her is a positive one - it's nearly impossible to do for every
experience, but avoiding situations where you have to catch or stress her will help.
I know a lot of people who have had a lot of success letting their shy bird come to them, just sitting near the cage and reading a book aloud so the bird can get used to your voice, sharing your meals from a distance and moving closer, always letting the bird have the choice of interacting with you or going back to the cage. I had a lot of success doing the latter two with my very shy linnie, I always kept her cage open and would offer her a chance to come over but if she ran back inside I would step back and away and let her come to me on her own terms. It took several months, but going slowly and being respectful of making her feel safe really helped - after those first few months, she rarely ran away anymore and started screaming if I didn't come fetch her
Hope all that helps! As far as earning their trust, it's very similar to tiels. The biggest difference I would say with quakers vs tiels is the cage aggression and their intelligence - not that quakers are smarter, but they seem to have a quicker wit, if that makes sense. More prone to puzzle solving, like opening their own cage, unhooking cage clips, flipping food dishes, etc. Little trouble makers! They're also very flock driven, making lots of flock contact calls and wanting to be included in everything to feel safe and comfortable. In the wild, they live in big community nests and are rarely alone and always calling to one another so some of that behavior carries over to home life as well.
We'd love to see photos or videos of her, once she's settled in! I love quaker voices, they really are one of the cutest species out there in my book
Sounds like you are off to a good start and I think, given some time, you and her will form a great relationship! So far your instinct in how to handle her is spot on