Why do we use "gubernatorial" as an adjective?
Both "govenor" and its adjective form, "gubernatorial", originally derive from the same Latin word "gubernare" (to govern) yet we use root "govern" in all contexts ("govern", "government", "governor", "governing", "governmental"...) except for "gubernatorial."
Why is "gubernatorial" the odd man out?
Also, is this just an American thing? In Australia, we also have governors but I've never heard the word used outside of the context of American politics.
Governor (dated 13th century) comes from gouernour (“personal keeper, protector, guide”), from the Old French governeor (11th century), itself form the Latin gubernator. The same can be said from other compounds with this root: govern comes from Old French governer, etc.
Gubernatorial, on the other hand, is more recent (dated 1734 by Etymonline) and was formed directly from the Latin root gubernator, hence the difference.
On the reason why thoses two didn't merge (or haven't merge yet, as they well may in the future), it's hard to say. It's worth noting that gubernator has seen a rare but continued used since the 15th century (1,2), and governatorial shows some increase in usage (though still rare) for the last century (3).
It is true that "governor" came from Latin, however, itwas influenced by French:
Origin: 1250–1300; Middle English governour < Old French governeor, gouverneur < Latin gubernātōrem, accusative of gubernātor = gubernā(re) to steer, govern + -tor -tor
The term "gubernatorial" is a result of Americanism, and is therefore a little different, even if it came from the same Latin roots:
Origin: 1725–35, Americanism ; < Latin gubernātōr- (stem of gubernātor ) steersman, governor + -ial
as well as
gubernatorial 1734, formed in Amer.Eng. from L. gubernator