I haven't drilled out a rivet on my WSM, but I have drilled out a LOT of rivets on my boats and RV.
In looking at the rivet, you want to use a 1/4" or 5/16" bit and drill from the inside. You are not actually drilling it out, but cutting the squeezed side of the rivet off so that it can be pulled or pushed through for removal.
Take it slowly and use no more pressure than you have to. If the bit snags the material, you could end up having the rivet just spinning in the hole and you'll be getting nowhere.
If the rivet does start spinning and you are having difficult removing material, try wedging something under the rivet head and old vent to help hold it in place (a flat bladed screwdriver might work). It may not be necessary to drill out the squished bit of metal entirely. If it gets thin enough, you might be able to take a pair of pliers and pinch what remains into a shape that is small enough to pass through the hole in the steel.
You'll do fine.
Chet