I used to work as a body piercer. My rule was not to pierce under 5years old. So if your daughter wants it then go for it (not that you needed my permission )
I used to use a gun (for lobes only) then started using the disposable ones once they got introduced. I agree with not going to essential beauty... They don't have good practices... I'm not sure of places in your area but I would look for somewhere that uses disposable guns and does one ear at a time. It might seem better to do both same time but if 1 goes off quicker and she flinches then other might not be in right spot. I've seen it happen all too often.