"Genderqueer" is a pretty broad label. Intentionally so, I think. Because of that, it's not something that's easy to pin down or explain.
One thing I would like to differentiate between is gender identity and gender presentation/performance, since that can get a little confusing when it comes to how the genderqueer label is applied. Some people include gender non-conforming behavior and styles under the genderqueer label. For example, some people might feel that a lesbian who identifies as a woman but is very butch can be genderqueer, because her gender presentation can be seen as queer. This sort of goes along with the idea that gender can be a performance.
But some people aren't comfortable with that because it can be interpreted as suggesting that being genderqueer isn't a gender identity like being male or female is. And for a lot of people, being genderqueer does mean identifying as something other than male or female, and experiencing varying degrees of gender dysphoria, similar to how FTM and MTF trans people feel. Personally, while I don't really mind "genderqueer" being applied to gender performance, I do get annoyed when people assume that I'm just a "masculine woman", because that's not why I identify as genderqueer (and I'm not even very stereotypically masculine!).
But since genderqueer is a very broad label, it's hard to say what's plausible or implausible in general. Some genderqueer people don't care much about pronouns, or don't mind using the pronouns for their assigned gender, but a lot of them do.
What I would recommend is to think about why and how your character identifies as genderqueer. What does it mean to her to be genderqueer? When she is in her male persona, is she hoping to pass as male, or is that not something she thinks about much? How does she see herself?
I'll have to see if I can think of any good resources. One book I can think of off the top of my head that I read recently and liked is
GenderQueer: Voices From Beyond the Sexual Binary. However, it looks like it might have limited availability since the new price on Amazon is very steep. Don't know if it went out of print or what.
Gender Outlaw: On Men, Women, and the Rest of Us by Kate Bornstein is a commonly-recommended book that you might like to look into. I own it but haven't read it in depth.
