I'd also agree with a lot of what has been said but taking everything into consideration, there should still be no reason why you can't pull of a respectable show in the time available.
Many will remember the Faking It series where a complete lay person passed himself off as a Pro after three or four weeks and yes, he did have a professional mentor but you're not aiming as high.
If you want to give it a go, and I wish you well if you do then go into it with a positive frame of mind and that will count for a lot. To be honest, for a WI gig much of what you need is charm, confidence, patter, confidence and good manners and they will most probably love you for that alone. Add a nice jacket, shirt and trousers and you'll look the part.
The magic doesn't need to be spectacular and you could do some basic coin, sponge and card routines that will keep you going for 45 minutes. Look at it as if you're going in for a marathon rather than a sprint so it'sa matter of pacing yourself.
Good luck
