I love being married! We'll celebrate our third wedding anniversary in a few months.
I got married pretty young. Met my husband when I was 21 & he was 28, got engaged at 22, then married when I was 23 & he was 31. We both knew early on that we wanted to get married, so getting married 2 years after we started dating worked for us. To answer your question, yes, I think it's normal to reach a point in your life, whether in a relationship or not, where you start having a strong desire to get engaged/married.
You think that desire is bad? Wait til after you get married and the BABY bug hits you! I was in the same boat before getting married. "I don't know if I want kids, and if I do, I don't want them for at least 5 more years" summed up the way I felt. It's weird how quickly that changed for me (and for most of my friends who are married). Granted, we are waiting 2 more years, so it really will be 5 years after marriage before we have a baby, but the baby bug hit me like a ton of bricks (much to my shock) just a few months after being married.
Long story short, I think you're at a fine age to get engaged. Getting married around 25/26 years old to somebody you've dated for years isn't unreasonable. My strongest recommendation is that people live on their own for awhile before getting married. Running your own household takes discipline and effort. I know that people do it, but for me, personally, I couldn't imagine going straight from my parents' house into a place with my husband. I matured a lot in the years where I lived on my own and supported myself with my own job and income. Good luck!