In becoming a genetic engineer, you'll need to develop a solid understanding of the fundamentals of biology and chemistry. As such, continue with your school work and pay special attention to your biology and chemistry courses. They might not talk about genetic engineering specifically but they do provide the basic framework and understanding for you to dive deeper into the topics that will lead you to genetic engineering.
I would also try to develop some experiences in horticulture and plants in general. Try working at a local nursery! Most schools that I know of do not have a nursery but I'm almost certain that your local town or city has a few. Their employees not necessarily have the background or expertise that will teach you about genetic engineering in plants but the nursery should have books and other materials that can teach you more about that topic. Just as importantly and just like learning about biology and chemistry in school, you can learn about the fundamentals of raising and sustaining plants. Different plants thrive in different environmental conditions. Some like direct light while others like indirect light. Temperature, humidity, soil acidity, amount of sunlight, amount of water drainage, water & soil nutrients are some of the factors that go into helping a plant thrive. You'll need to know about those qualities at some point if you want to mix and match genetic material between plants while helping them grow up and thrive.
As for higher education, you can certainly begin by looking into schools that specialize in horticulture and bioengineering. It might be difficult but it's possible for schools to specialize in genetic engineering for plants. I don't think you'll find an entire university devoted to genetic engineering for plants but you will find departments and schools (within the university) that will tackle these projects. More likely than not, you'll find small research projects that work on genetic engineering for plants.
Lastly, I would look into the following companies since they completely or partially work in the field of genetic engineering for plants:
- Monsanto (seeds and genomics)
- Dow Chemical Company (they do all sorts of stuff)
- Evogene Ltd. (agricultural genomics)
- Syngenta (seed and chemical supplier)
- Agrium (retail fertilizer supplier)
- American Vanguard (herbicide and insecticide producer)
- CF Industries Holdings (fertilizer)
There are a lot more companies out there who can provide more information about how to get started in the field.
Best of luck to you!