I have two children of my own. One is three and the other, three months. One is a slow mover compared to an adult and the other is completely immobile. Any adult by that description would be a danger to your survival should you chose to take them in. So you have a moral choice to make. Bring them and feel good about yourself or do what you can and leave them. Your not going to sleep well anyway.
Children, on the other hand, are defenseless by nature and have to be kept safe no matter what the cost for the greater good of mankind. Taking on younger members to your team is a risky endeavor but a worthwhile investment for humanity.
Part one :
I would welcome any child aged eight to thirteen into my survival group as a valuable member. At that age, they can run fast without tripping over their own feet and can grasp the basic fundamentals of survival. You can teach an eight year old how to shoot, defend his or her self, make a camp, and fortify a safe house among other things. And maybe the most important trait a child has is their tendency to follow the lead of an adult and take orders without question. You wouldn't have to worry about a power struggle.
There's really no easy answer. Remember that you are trying to survive yourself. I would do what I could to help the child aside from getting infected. Too many children meet their fate in the maw of those they once trusted and loved. If you really value the lives of the children you have in your care, first and foremost, keep them hidden, safe and close at all times!