Not sure where you get the idea you would need three years worth of jabs, all you would need is the full initial course which is two jabs, although you only really need a booster which is one jab, if you are sure she was done as a puppy.
Probably best to get the full course to be on the safe side.
The microchip number can be read by a vet or anyone with a scanner, although this will only give the number, and although the chip company will have the name and address of the previous owner it will not have any vet details.
It would be a good idea to get the microchip number transferred to your name and address though, in case she goes missing. The vet will put you in touch with which company she was chipped with.
Can you not check with any vets local to where you got her from, as they will have her chip number on her records and will probably have chipped her themselves.
Do you know her pedigree name? Her chip details might be on her KC registration document.