hummingbird I think it is an amazing thing that you are considering this and you have my utmost respect. I also think you have been given some very good advice on here with lots of different points to think about.
I have been mulling over your dilemma and have a few thoughts that may or may not be helpful. I am really not trying to influence your decision in any way - in your situation, I'm really not sure what I would do, so feel free to disregard my musings.
1) Foster placements of teenagers have a very high breakdown rate, for a number of reasons. Your little friend may be lucky and be placed with experienced foster carers who are a good 'match' and be settled there for the rest of her childhood. On the other hand, with the shortage of foster carers she could find herself with inexperienced carers with limited support. What I am saying is that foster care doesn't bring any guarantee of stability.
2) 'Family and friend' placements, such as with you, have a higher success rate and lower breakdown rate than mainstream foster placements, for a variety of reasons. Carers are committed to the particular child, and the child generally wants to be there. So the chances of a placement working out are statistically higher than the chances of a stranger foster placement working out. That's no guarantee of course and statistics are not much use when feelings are involved.
3) When you see the SW ask her if you could be assessed as Family and Friend foster carers so that you can be given the training, support and backup that all foster carers receive. If this is not an option ask why not, since the girl will be a looked after child without that. (That's not to say that you must accept this option, but you need to know whether it is an option at all).
4) It says everything that you are worried about the girl facing another rejection if it doesn't work out. Of course that would be awful for everyone. However - just a thought - if she already knows you are considering this she may see it as a rejection if it doesn't go ahead, so in that sense you have nothing to lose by trying. I do not mean to minimise the commitment this will need but just trying to look at it from the girl's point of view.
I would still say, think it over very, very carefully. I'm not sure I would have the energy to see a teenager through to independence but on the other hand there are many older foster carers who seem to thrive on the challenge. Whatever you do, try to talk to the girl about the process and try to involve her in the decision so that she can understand how much you care about her, even if you don't feel able to look after her.
All the very best, I'm sure you will stay involved in her life whatever happens and she is very lucky to have you (poor child has not been very lucky with much so far, has she?)