I started out with an 8-mile round-trip to the Post Office a couple of days a week. My first target speed was about 10 mph, which as it turned out was sort of easy.
My first problem was a sore butt, which just takes regular riding at almost any distance to help (sort of). Sounds like you're already past that point.
My second problem was being wiped out after the ride. It wasn't so much physical ability as it was that my body was not used to processing that much glycogen. (Triathletes say nutrition is the fourth discipline.) A tall glass of milk (or chocolate milk) immediately after your ride can help that quite a bit.
Your body craves carbs to replenish the glycogen, and protein helps things rebuild. You don't need a lot, something like 200-300 calories of mostly carbs and maybe 10 g of protein. Milk happens to fit those requirements really well, and it's cheaper than sports drinks. But you do want to have something right away, or your body can go into "wiped out" mode and stay there for hours. Not good in a work environment.
Anyway, I say jump in and do the ride. A trial run is smart, but regardless, just take it easy and see how it goes. Before you know it you'll be riding every day.