mamadoc - I have 30 years experience in social work, as a child protection worker, and manager of a fostering team. If a Care Order is made the LA do have a duty to see if there are relatives or friends who can care for the child. How old is this child by the way.
Sorry but I can see all sorts of problems ahead, which others have mentioned. If a Care Order is made it really means that the mother is unfit to care for her child though she will probably be allowed contact,which may be supervised. However your friend is almost certainly going to press you for more contact or take to popping over to see her child, which is going to put you in a very difficult position.
I am also concerned that the child in question is older than your own child - and has behaviour problems undoubtedly caused by her mother's poor parenting. I think you need to be realistic about this, and your own child could become very unhappy with an arrangement especially as the child is older. What is the age difference?
If this child is not going to be returned to the care of her mother, then yes she is going to need a permanent family BUT that is not your problem. You must think of yourself and you own child first and foremost and don't let your heart over rule your head.
Also anyone putting themselves forward to take over the permanent care of a child has to be thoroughly assessed by a social worker and every nook and cranny of your life is looked into. You may find this helpful though because you will (if you go ahead) talk in depth about the child and the pros and cons of taking over her care. The assessing sw then has to make a recommendation to the fostering panel about your suitability (or otherwise) and of course the reality is that you won't know whether it is going to work until it happens.
My advice for what it's worth is to steer clear - I think there are just too many problem areas for it to have a good chance of being successful.