For what it's worth, my daughter didn't choose a dominant hand until she was halfway through kindergarten, and she's doing fine. Her fine motor skills did develop more slowly than is average, but her preschool and kindergarten teachers told me that as long as she was progressing, I shouldn't worry, and indeed now, at age 7 (second grade), she is where she should be developmentally. (She finally settled on being a right-hander, but is still fairly adroit with her left.)
I know that one person's experience is not a substitute for data-supported information, but I hope that our experience gives you some peace of mind.
If you are still concerned after you hear from everybody on this forum, your pediatrician might be a good person to ask.