You are not doing anything wrong by dating. You are absolutely entitled to adult companionship. As others have said, just don't introduce your daughter to anyone until you're sure they'll be a long-term presence in her life. I think it's unrealistic that you will wait until you're engaged to someone. (After all, how can you agree to marry someone before you see how they interact with your child?) But, the important thing is NOT to bring home a different guy each week...or even each month. Date someone steadily for several months before you bring your child into it.
I'm a single mom, too, and I've been in your shoes. I understand the guilt you're feeling, but you're human. If you feel ready to date, then by all means, date.
I've been dating a wonderful man for a year now. He adores my girls (7 and 4), and they adore him too. He has 4 children of his own, and all of the kids (his and mine) get along great. Even now, though, there is no guarantee that we'll be together forever. But you know what? This is real life, and there are no guarantees. It's OK for kids to see that. Live your life!