Jim and bigbryce are correct: a 7mm-06 is not a .280 Remington.

A word of caution: unless you have loading dies for your rifle--dies that you know work because you've seen and fired ammo in your sporterized 03 rifle produced specifically by those dies--then you're faced with a dilemna regarding obtaining and/or making handloads for your rifle.

One option is to take your rifle to a very experienced gunsmith and have him make or order dies for your rifle, at which point you would then need to read P.O. Ackley's Handbooks for Shooters and Reloaders, Vol. I and II, to learn about the 7mm-06 and proper starting loads for it. The other option is to simply yank the old barrel off the rifle and put another barrel on it--which does not have to be an expensive venture--see E.R. Shaw barrels or Douglas barrels online--chambered in the "known" caliber of your choice, say .280 Remington, or 7x57 Mauser, or 7mm Remington Magnum, or whatever suits your fancy. (I put at least one new barrel on one of my rifles every year.)

One last note: you should probably have an experienced gunsmith check the serial number on the action of your 03 rifle and determine what year it was made, and by which manufacturer. Some year groups produced 03s that are not nearly as strong as other year groups, which could become an important issue if you intend to load and shoot high-pressure (60,000-65,000 psi) loads in your rifle. Any experienced gunsmith has the information on hand or can obtain it with little effort. Just a thought.

Basically the 7mm-06 and the 280 can be the same. You just need to take it to a gun smith and have a casting of the chamber to measure the dimensions.

Also need to check the serial numbers to se if its properly heat treated as Mr T.W. Davidson has said.