Well yes, but I think she would make the decision herself anyways now that she runs the whole school.

 

I would remove Divination completely and if that isn't possible then I would restructure to accept only people that are seers. And if that isn't possible then I would completely change the course to go from predicting the future to something akin to the skills that Sherlock Holmes/Patrick Jane/Shawn Spencer possess. Legilimency and Occlumency could probably be incorporated as well. And the teacher I would have for this would be Dumbledore himself (Due to his skills in the in both arts).

Binns, I would replace with Hermione. As if she's going to let anyone sleep in her class. Then again, she could probably teach any class successfully.

Snape should theoretically be replaceable with anyone. And I don't mean that as an insult to Snape (Except I do) but all he literally does is tell them to read the instructions in the textbook or write up the instructions on the board (Presumably copied from the textbook). Anyone can do that.

Defence could maybe be taught by Harry though I would prefer it be someone who was an ex-Auror, maybe Kingsley.

 

I'd basically do as you say,

Potions -> Slughorn

History -> Doge or someone else who is actually alive.

Divination -> Replace with Astrology (or whatever centaur divination is called) with Firenze and keep Trelawney on as a tutor for actual seers.

Defense -> Split in three:
Defense Against Magical Creatures -> Lupin
Defense Against Dark Wizards -> Moody
Duelling Elective -> Rotation of Moody/Flitwick/McGonnagal

Defense against creatures and dark wizards seems fairly different and having Moody teach DADW, probably only starting 3rd year or so, while Lupin teaches DAMC seems like a good idea. Dueling could incorporate the spells/concept from the three primary casting teachers (Defense/Charms/Transfiguration) into combat.

Of course, they're a bunch of other things such as muggle studies, runes, and arithimancy that the books don't really cover beyond saying hermione takes them. Considering the general state of wizard awareness of the muggle world an expanded muggle studies programs seems like it might be a good idea.

 

If Nicholas Flamel was still alive, he could be pretty good history or potions teacher.