Can you divert a brook?

All you should need to do is channel out the desired path.

If you want to re-route the brook and not simply fork it into two, you have a couple of options.

The easiest is if you're in a climate that freezes. Wait for things to freeze over and you can dig out the ice like any stone and erect walls to block the path of the water.

If your climate doesn't get chilly enough for that, I've heard with enough operating pumps you can remove water from a brook faster than it is naturally replaced. This should allow you to run the brook dry long enough for you to again build a wall blocking the water's original path.

Then it should simply be a matter of digging out the path you want the brook to take all the way past your fortress and back to the original exit.

One note: brooks naturally have a kind of layer over top which makes it possible for your dwarves to walk over it. Your diverted brook will not have this layer and dwarves will not be able to walk on it. So keep that in mind: you may need bridges.