If your goal is to lose weight and gain fitness you are golden. Running a 5k in September is a piece of cake. The only question is what time will you be satisfied with?
It sounds like you are going about it the right way by walking first. Just keep building up the length of the walk and start adding in some running. By September you should be easily able to run a 5k.
The key to your whole goal is race time goals. If your goal is to finish without regard to time you can do that easily.
A word of caution. Progess in the beginning is rapid and you'll soon start feeling more energy. Don't get carried away and start thinking that you can push your routine. Slowly but surely avoids injury. Injury is the worst set back that can happen.
Good luck and let us know how it goes.
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