Ya know, I think a Prime Minister would make sense in Equestria. Much like the United Kingdom there is an elected Prime Minister who is the head of Her Majesty's government.
Mostly the Queen's job is just to approve things that the government does. Seems like something Equestria might do.
In Australia this is also the case. The Queen is technically still the head of state in Australia. She is represented by the Governor General, who is like a proxy for her wishes. In reality the Governor General's job is pretty much to rubber stamp whatever the government decides to do though.
Anyway, looks like Dash is regretting her victory.
"Draw a pony ruling/Draw a pony plotting"