When correcting harmful behavior in a child, it’s important to have very clear expectations and consistent and meaningful consequences when those expectations are not met. Addressing problem behavior early on is critical; while it takes more time up front, it will pay off in less resistance against established expectations as the child grows up.
That being said, your daughter’s comments about wanting to kill herself are very concerning and should not be ignored. At this young age, she should be monitored at all times. Even if she is in her room, you should check on her at least every 15 minutes. Even at age 6, she could put herself in danger if not monitored.
Communicate clear boundaries to your daughter and patiently yet firmly correct her when she crosses those boundaries. You also should seek help from a professional counselor to find out why your daughter is expressing a desire to harm herself.