Annoyed with a co-worker

I work with a woman who is supposed to support our team. Our organization runs very lean and we didn’t have the budget to hire a junior analyst instead of an assistant, and there is a major difference in what the two would be able to accomplish. During the day, I’m usually very busy and don’t have time for her interruptions. Usually, I would think that an assistant is trying to help, but her questions feel really stupid to me and she asks a lot of basic things even after being in the job for a year. Her mentality is a more cover-your-ass mentality versus how-can-I-make things-easier-for-the-team mentality. She’s always asking me to verify what to do with a yes or no email so she can cover her ass. I find her to be highly annoying, stupid and lazy. I hate interacting with her. She feels more like an obstacle than an assistant and I’m dying for someone with more intelligence to come help me so that way my workload can be easier, but I don’t make the hiring decisions, so I’m stuck with her. She is kind of passive and doesn’t add the value that I wish she would add.

C: F sends an email asking whether she can send a loan for booking
T: I can’t believe she’s asking me this question every time she books a loan
F: Irritated
A: Respond to the email, try to avoid her, dislike interacting with her any more than I have to, consider her messages to me to be interruptions, call her an idiot in my head for continuing to ask me questions that she should just not ask because she should know her job after 18 months in the role, pretend to be nice when I can’t stand her
R: Make the work environment even more stressful for myself

C: Same
T: She is not trying to impede my workflow
F: Calm
A: Have a conversation with her about which emails would be helpful and which emails are not and why, ask her to send me communications at only certain points in the day, ask her what training she needs to be more confident in her role
R: Have a more productive assistant

I’m not her boss, so I’m not even sure it would be appropriate for me to do this, but I really need her to pull more weight, so I need to pull more weight to train her and get her up to speed.