When I first started biking to work (4 years ago), it took me about 50 minutes and I averaged 12.1 mph on a typical day. Last week, I had my best time with 35 minutes for an average speed of 17.3 mph. Most days I'm around 38 minutes and 16 mph.
Hills, stop signs and wind are always going to be a major drag on your average speed. It takes an awful lot of riding at 20+ mph to make up for the 30 seconds or so that you spend coming to a stop and then getting back up to speed, but you'll be able to "flatten out" many of your hills as your fitness improves. The hard ceiling imposed by your heart rate probably won't last through your first year.