CPU usage and load average are two different items. The load average is the average number of processes which are in a state that they could run, but they don't necessarily use the CPU at that moment. Processes which are waiting for disk I/O are counted in the load average for example but they don't use the CPU.
On systems with a lot of I/O you can therefore have a high load average with an almost idle CPU. If the CPU usage stays far below 100% continuously there is no reason to upgrade the CPU. But if the load average stays often above about three times the number of CPU cores, you may want to optimize your system. In many circumstances optimizing the I/O hardware (adding a RAID controller with battery backed up write cache for example) will have more effect on the load average than adding more CPU power.
And the short answer is, those numbers look fine, I wouldn't upgrade.
If you need to upgrade, it's normally obvious by slow loading web pages. I expect your web pages are loading fine.
Many years ago my numbers were basically idle all the time - anything over 1 or 2% load was rare. Today my server (which does have multiple CPU's) floats at roughly what yours does, and I have no intentions of upgrading - even though the server is probably 5+ years old.
Actually this thread prompted me to check. Looks like the server is actually about 6 to 6.5 years old. And it wasn't top of the line then, though it wasn't bad. Still chugging along no problems. Looks like I can get them used now for $250. That's a drop of 10 fold from when I bought them!
After 6 years you may slowly run into component life time problems. Mechanical components like the disks and fans are probably the first to fail. But besides that, older single core systems like the one the OP mentions are performance wise good enough for most web serving tasks.