Most vets don't specialize soley in cats. If you want to do cats, then you'd probably have to do dogs as well.
After high school it will require 6-8 years of education. 2-4 years of undergraduate pre-vet coursework. You can apply without a bachelor's degree, but your chances of acceptance are increased if you have a 4 year degree. Then, assuming you're accepted vet school is four years.
The courses you'll have to take in college, before vet school will be a lot of science courses. I've included a link to a website that lists all 28 US vet schools and their requirements to give you an idea of the coursework. It'll be a lot of biology, chemistry and physics.
You will have to maintain an average of 3.5 or higher. The average GPA of admitted students is typically 3.5.
You will also have to take the GRE. Some schools do require the MCAT or VCAT, but the majority require the GRE. The GRE is similar to the SAT and tests your basic reading, writing and math skills.
You will also need both general animal experience and veterinary experience. You're still pretty young, but for general animal experience you can think about volunteering at a local zoo, animal shelter or wildlife rehab facility. For your veterinary experience you'll need to work for a vet. You're definitely too young for that now, but most clinics will hire at 16 and some at 15. Most will let you start to shadow at 14. So, call around to some clinics and ask if you can shadow and if not, when you'd be able to. Once they know you're interested and you've started shadowing you'll be first on their list when an afterschool job becomes available. It'll start out as a lot of walking dogs and cleaning up after the animals, but as you get older, they'll let you do more.
Hope that helps with some things you can start thinking about now.
Also, even though you want to do small animals, vet schools like to see people that are well rounded and open to anything. So, think about getting some large animal experience as well. You never know you might change your mind.
Speaking from (a ton of) experience, it's very possible. Every cat reacts differently to the disease but I have had cats with feline leukemia who went on to live happily for many years. One cat in particular had lost a lot of weight, was extremely pale and lethargic and had an eye that turned blood red; the vet tried to convince me to euthanize him but started him on antibiotics when I insisted. He perked up, gained back the weight, and went back to being his loving self. I would never listen to people who say there is no hope for cats with feline leukemia; they might have ups and downs in their health but they often have many happy years left ahead of them!