The impact of running is hard on the body, as a force of 3-4 times your bodyweight goes through your legs as each step lands. And obviously more weight = more impact.
Your leg muscles and tendons do adapt to the impact, but it does take time.
It is generally recommended that you build up a solid walking base (2-3 months) before transitioning to running. And then when you do transition to running, a Couch to 5K plan www.sparkpeople.com/resource/fitness_artic
is definitely the way to go.
But I understand that pride is involved, and that you want to prove your friends and the doubters wrong.
My advice would be to start walking now - 3-5 times per week. Hopefully in a few weeks you are walking 5K comfortably. And if you are feeling comfortable by 14th September, you can perhaps try week 1 of C25K, so that you can at least run a few 1 minute intervals by the 21st.
Also, keep your running speed down at this stage - less speed = less impact. You should aim at a pace that is not all that much faster than your fastest walking pace.
When it comes to running, run no more than 3 times per week (to allow your muscle to recover from the impact and get stronger), although it is fine to do some lower impact exercise (eg. walking, cycling, elliptical) on non-running days. But do include a genuine rest day at least once per week.
And one other suggestion. Having built up this momentum for Sept 21st, don't waste it. See if you can find a Turkey Trot in your area in late November, so that you have a motivation to continue with the rest of C25K.