It's never too early to start gun safety IMO. I started carrying my liluns around in a sling to gun shows as soon as they came out. It's about acclimatizing, and taking the novelty off. They get practiced at being around guns and not touching. I also took them with me to the range as soon as their ears would fit hearing protection.
As soon as they're old enough to know what a gun is is when I started them on more detailed safety. At 3ish, I could tell my youngest all day long "don't play with guns", but she wouldn't distinguish Daddy's revolver on his hip from a semiauto HG or a rifle. As soon as she could recognize when I asked her "What is that?" is when I started on why they are dangerous and why not to touch them.
I agree with Cornered Cat as a resource. I disagree on using toy guns for training. Like someone said, they learn "muscle memory". That means if they're used to running around with their finger on the trigger, that's the way they'll train. We don't allow "gun games" in our house. You don't practice/play pointing guns at eachother. I'll buy my girls all the real guns they want, but I significantly discourage playing with toy guns. If you can monitor them to make sure they practice muzzle control, that's great, but I don't like guns being treated like "toys".
I also disagree that a 6yo can't understand "death". It depends on how they're raised. Today's kids have certainly been desensitzed to violence and its seriousness and are sheltered away from a lot of unpleasantness. But if "death" isn't hidden from them, they can fully grasp its finality. My kids go with us to family funerals and understand what's happened. They've helped/watched me clean game since they walk. The oldest (6) was helping me with some pheasants recently. I showed her the shotgun damage and asked her what she thought a gun would do to her or her sister or her friends.
I took the oldest to a defensive pistol match and she didn't cope well with the .45s going off indoors. She'll build up to it. She's eager to learn, though. She's working with an airgun, but is still 2 years too young for 4H shoothing sports.