The battery might have a pop out label which shows when it was placed in service. Before replacing the battery, I'd clean the terminals, check the water, charge it and replace in the tractor. Check the voltage before cranking. If you have a partner, check the voltage while cranking and see the drop. Then check again when the engine is running.
After charging it should be somewhere between 12.4 and 12.8 volts. Expect several volt drop while cranking but I would guess not below 9 V. Running voltage should be above 13 and possibly as high as 14. If it's not above 13 when running you may have a charging issue.
Don't overlook the impact of dirty terminals. It not only affects the ability to crank but can prevent the charging system from fully charging the battery. Frequently older equipment has replacement, clamp on terminals where the wire goes into a clamp. Those can look fine but if you loosen the wire clamp, the wire is all corroded and doesn't make a good electrical connection with the terminal. An of course, the battery to terminal connections should be clean as well. Also check the ground connection to the frame. Corrosion there is just as bad as corrosion on the hot side.
You might need a battery but even if you do, having all the connections clean will help the new battery as well.
Treefarmer