I've been mulling over this question for a while before replying. And I think that yes, realistically, I would likely hesitate.
First we have to define "child" though. To me, "child" means someone pre-pubescent, not a "child" as the antis use it meaning someone as old as early 20s.
So why would I hesitate? Same reason I have given in saying that I would be more hesitant shooting a dog than a bad guy. Mens rea. Obviously we are speaking in general terms here, not about some blood streaked 11 year old mesomorph who looks like an enlarged "Chucky". Also, there are differences in the sort of threat. If I just saw the child shoot someone purposefully, then a threat is a threat. But if a child just points a gun at me, even if saying its a robbery, then yes, I think I am going to hesitate to try to determine if it is a real gun and ensure that it is a real threat and not just some dumb kid pulling a very dangerous, potentially lethal (for him) prank.
By the time a human is obviously teen aged I expect him/her to know and comprehend the potential lethal risk of threatening with anything that could be reasonably construed as a real firearm. If not, that is on Darwin, not me. However, a younger kid may not yet have that developed sense. A 10-11-12 year old may not have that cognitive reach to have thought through the implications. By the same reasoning, I also would be hesitant to use deadly force in a similar scenario against someone with Down's Syndrome for example.
I think those who have actually faced combat and self-defense situations have well established for us all that one does not know what one will do when actually faced with a lethal threat but that doesn't negate the validity of thinking about such things as the mental exercise can be as valuable as the range time. In that vein, I'll admit that I had never thought about this particular question before. I look forward to reading more responses and will certainly be mulling through scenarios about this for a while.