I do is put my laptop into a large zip-lock bag and put that inside a small backpack (for padding) and stuff it into my pannier. Works like a charm.
+1. I was going to add that for a 2.3 mile commute, you don't really need to worry or overthink too much. If it starts raining, just haul ass and you'll get to your destination either way pretty quickly. If you had a commute 4-5 times longer you'd probably want to consider fenders, rain gear, quality lights, possibly gearing, quality of panniers, etc....this is IME anyway, I don't speak for other folks.
BTW - I ride by Arlington National Cemetary daily but I doubt I'll find your plug
.