You'll be taking orgo because all vet schools require that, and then taking biochem is a must for most schools. There are typically two types of biochem offered at college... One which is a version without a lab, and usually is only one semester long. Or there is the version with a lab, and it takes a year to complete as they go more indepth in the subject.
The lowest level of biochem course should be acceptable anywhere to count for the biochem pre-req necessary at vet schools, so long as it covers "examination of the structure and function of major biomolecules; chemical and physical properties of nucleic acids, proteins, carbohydrates, and lipids; gene replication and expression; biochemical energetics; principles of enzyme kinetics; vitamins and coenzymes; pH and buffers; and an examination of primary metabolic pathways in the mammalian organism." That's taken from the Tufts vet website, but all the other ones that ask for biochem basically say the same thing. So... as long as the class goes over those topics, you'll be fine.