Your vet is most likely advising you in accordance with the laws in your state. In Massachusetts the law says that the first rabies shot must be given by 6 mos. of age, a 1-year booster must be given on or before the 1-year anniversary of the initial rabies shot, then the dog gets rabies shot every 3 years. If I miss that 1-year anniversary by even 1 day the vet is required by law to give the dog another 1-year vaccine. So I pay very careful attention to rabies due dates. In fact I've created a log in excel showing dog name, date of rabies shot, duration (1 yr. or 3 yr.), next due date. Every time I update the log I print it out and put it in the front of my "vet records" book.
And about my vet records book, I use a 3-ring binder, the first page (in a page protector) is the vaccination log, then I have a tab for each dog, the first page (in a page protector) is the dog's AKC registration, the backside of that page is the pedigree and AKC Champion certificate, the next page is the current rabies certificate with rabies tag taped to it (with all the previous rabies certificates behind the current one), then the town license certificate with license tag taped to it (and all previous ones behind it), then the microchip certificate, then every vet visit record from the beginning of time, and lastly the AKC-required breeding records, if applicable. With multiple dogs, this binder has been a blessing. I've only ever had to make one trip to an emergency animal hospital, had no idea what they might ask for in the way of prior medical info on the dog, so grabbed the binder and the dog and hurried out the door. When I got to the hospital the both the receptionist's and the vet's jaws dropped when the saw my medical info. It might sound like overkill to some, but I can find what I need when I need it just by turning a page.