To become a Vet. requires more than just passing a single test (dependent, of course, on your local regulations). You will probably need a B.Sc undergraduate before being accepting into a graduate Veterinary Medicine programme.
Despite what most of your Secondary School teachers will tell you, you do NOT need a high school diploma to enter into university. You will need to check the entrance requirements into the Universities of your choice. As long as you have those courses required to enter, and you've completed them at a sufficient level of achievement, then you can get into the school. there's no age requirement and there's no requirement to "complete" high school. But that's just the entrance. You will still need to pass all the relevant Uni course to receive your degrees. So if you focused your high school subjects on only those required for Uni acceptance (guessing: chemistry, biology, mathematics, and English, you don't NEED Art or History) you could skip 1~2 years of high school, with the understanding that you will be missing the opportunity to become a well rounded individual which is what is most appealing to the majority of people you will interact with later in life.
So you could get started on Uni credit through the IB high school programme.
http://en.wikipedia.org/wiki/International_Baccalaureate
You need to research what exactly you need to accomplish to become a Vet. Start by drawing up a big flow chart with becoming a Vet. as the Goal at the top and work down:
EXAMPLE (based upon my engineering requirements):
1) Getting a Vet License Requires:
-practical experience of 4 years
-Vet. Diploma from an Accredited Uni.
-completion of a professional test
2) Veterinarian Graduate School Requires:
-undergraduate science degree with 3.5 GPA minimum
-high placement on entrance exam (Vet. MCAT?)
3) Science Undergrad Requires:
-so on and so on
4) Entrance requirements for Uni:
-so on and so on
Keep in mind however, that most decentUniversities will look at your entire application package (extra-curricular and philanthropic activities for example) and not just your grades, so as I said earlier... it is possible to start now, but you need to really research your future schools and tailor your high school courses specifically for your goals.
So to answer your question: NO.
But, hopefully I've pointed you somewhere you can get started. Good luck.