Youve just got lots of work to do. Slick tires vs. knobbies does make a difference but its just about time in the saddle.
When i first started riding, i had to work hard to keep a steady 16-17mph on a bike path. At the time, that felt pretty tough. Now, thats a very liesurely pace.
Just focus on riding more and being comfortable on the bike. Work on increasing your mileage and the speed will come. As a new rider, you will get faster naturally just by riding more.