Driving is intimidating for many. I wouldn't push it. What is your reason for urging her? There is no rule that every teen who is eligible for something has to actually do it. That's actually a good lesson for high school in general - just because "everyone" is driving (or dating or going to the prom or drinking or vaping...) doesn't mean she has to. Wait it out, stop pushing. By high school, kids have to advocate for themselves, talk to their own teachers, be responsible for their own assignments & lunches & supplies, and so on.
Now, does her depression stop her from doing other things? Is she not completing other things? Task completion is a huge problem with depression, so if you see this across the board, then she either needs treatment (if she's not getting any) or more treatment (counseling, perhaps medications, alternative therapies) if she's already doing something. Moreover, attention disorders can be a barrier to things like driving that require great concentration.
Your daughter may not know how to organize her thoughts enough to research driving schools, but her friends are going to be doing it and talking about it, so she can inquire that way if she's interested. The school may have a program or at least information on them - a couple of driving schools in my area pick up at the high school at the end of classes, for example.
If your daughter is growing and maturing in her level of responsibility in other areas, if she is mastering life skills, that's good. If she's not, then it's time to negotiate with her on the things she needs to know to be a functioning adult. Does she do her own laundry? Does she cooperate and do family laundry, family chores? Can she function in a kitchen besides opening a bag of chips? Can she set the table, help prepare meals, wash dishes? Can she replace windshield washer fluid and put gas in the family car? Can she start and push a lawnmower? Is she starting to learn what things cost (groceries, electricity, cable, cell phone, clothes, insurance)? Does she work at all, even part time, in the neighborhood (walking dogs, weeding gardens, babysitting, taking in packages/mail for those on vacation)? If not, start with some of those things. She will feel more confident as she succeeds, and she will have the know-how and worldview she will need for college or the working world.