In general Eucalyptus shouldn't be staked, because flexing in the wind is important for them to gain strength. If it had been grown in the ground from small it would never have needed one. But as you have one that is pot grown to 6ft, it probably needed some support to start with as it hadn't put down roots deep enough to support itself, nor developed the trunk strength. So if it looks like it can now support itself, I'd say take it out. Sadly, Eucs that are grown too long in pots sometimes never obtain the roots to support the top growth (stake or no stake), and are prone to being blown over in strong winds. You could shorten it, but then it would develop multiple stems from the point you cut it, and that may not be what you want.

Do you know what kind it is? Some of them, for example the very common gunnii, grow very big and fast.