Brooke, just get started and improve as much as you can between now and then. If you don't like the score you get at NASS, I'm pretty sure you can take it later, allowing you several more months to get where you want to be. Maybe you could get a book like "You Are Your Own Gym" that focuses on strength training. Also, work your way into running.
If you can't do regular push-ups yet, you could start by using a step, chair, table, or even a wall and doing push-ups with your hands elevated. Then lower the elevation as you get stronger. Soon, you'll be able to do them on the floor. When you hit failure on the floor, add in a few more with your hands elevated. If they get easy on the floor, you can make them harder by elevating your feet.
Start working on the running by warming up with a fast walk, running what you can, then switching back to walking when you have to. Alternate until you've met your mileage goal. Try to run farther without walking each time. Pretty soon, you'll be able to meet your mileage goal without walking.
I talked about how to work on pull-ups on the other NASS thread if you need a plan to reach that goal.
Good luck. You can do it.