There will be more choices with major hotel chains that offer restaurants in their establishments in Brandon than the smaller Cities and Towns you mentioned (Minnedosa, Dauphin, Neepawa, Shoal Lake).
Having said that there might be a few more options in Brandon if some of the below thread is true. One would have to call a place if you wanted to find out if they are open 2018 Christmas Day. This link is the same kind of question last year on ebrandon in December of 2017. I'd definitely call around to avoid a locked door, though. Don't assume anything.
A phone call and reservations might be recommended. You'd be surprised at how many people dine out Christmas Eve, Christmas Day and Boxing Day.
Here is the ebrandon Link for 2017 Christmas.
http://www.ebrandon.ca/messagethread.aspx?message_id=999965&cat_id=315
I hope you enjoy a fuss-free Christmas where someone else can look after the dishes and you can relax.