Do you serve a separate dessert at brunch?

If you want to go the dessert route (who doesn't love something sweet to cap off a nice meal!) than maybe have a small selection of cookies/pastries/whatever fits your theme. I doubt you need to go all out on the dessert if the brunch meal was hearty enough. Something small should suffice.

If you don't have a sweet dish at your brunch table, then add a dessert. For me (who is more inclined to have savory for brunch), sticky buns and sweeter scones (like maple glazed, actually any glazed scone) are dessert. I don't it is obligatory to have dessert at brunch. Sounds like you have a rather good selection of sweet and savory, so don't sweat it.

Sure, why not? I'm sure someone will be happy to eat it.

A lot of American breakfast items are really desserts, but Americans are in denial.

Most breakfast pastries are really cakes that aren't call cake. Pancakes despite their name are not considered a cake, but they and waffles are cousins to crêpes. The classic crêpes Suzette dessert isn't much different than American style pancakes.

Doughnuts are breakfast items, beignets are dessert items but they are closely related.

Just get over the "dessert" moniker. Americans already eat dessert for breakfast anyhow, they just don't like calling it dessert even if they really are.

If you go to a fancy hotel's breakfast buffet, they will have cake anyhow.

Most importantly, do what you think will please your specific guests, not what random commenters on some anonymous Q&A forum think.

Best of luck.

Brunch, as one of the least structured meals of the week, has few shoulds.
Also, they range from casual and small to fancy and large.
For the casual and small, do what you and your guests like. With dishes like scones, perhaps, fruit salad, waffles and/or pancakes already included, there is no need for a separate dessert.
If you have a larger, fancier brunch, perhaps for a celebration or a family occasion, maybe present two buffet tables at the same time, one for savory and one for sweet dishes. That way people can have what they want, when they are ready for it. And/or concentrate on the one table that has more of what they like.
Last, have a look at cookbooks or online for brunch menus, from writers or chefs whose work you like. Food Network (love it or hate it) also has a selection of brunch dishes from its cooks/shows.