You sound pretty dedicated, so no sugar coating this - at +30% body fat as a male, you are pretty big and thats going to make this hard.
To achieve your goal there are two things you need to get in order - your diet and your running. Now, I'm assuming your goal is just hitting that timeframe.
There are lots of resources here and elsewhere that cover diets, must first and foremost, start tracking it. Calculate your Total Daily Energy Expenditure, and aim for at least a 100-200 Calorie deficit every day. Every pound you carry that isn't in your legs will make your running harder. The easiest way to drop your Calorie intake is to minimise your sugar intake. It sucks, but you need to do this.
Now some good news, your target 1.5 miles in 15 minutes is relatively "easy" by running standards - you're aiming for a 10 minute/mile, whereas peak runners do it in under half this. Normally, I'd recommend a nice Couch25K program, but you don't need to run 5Km you need to run about half that.
What you need is milage and consistancy. If you are doing 12 minute/miles there is a good chance you are walking some of the way.
Once a week do a 1.5 miles continuous, no breaks. The aim of this isn't to be fast, but to be consistant. Record your time each week and that becomes your pace to beat. You need to shed 8 minutes off your time in 2 months, which is about 30 seconds per week which is certainly achievable.
Also, three days a week do a the following:
0.5 mile run (fast as possible) / 0.5 mile walk (recovery) * 3 for a total of 1.5 miles of running and 1.5 miles of walking.
The aim of this is to get you used to running fast, so make your runs fast, faster than the pace of your long run.
You'll want to have a day of recovery before your long run, so a program like this:
- Monday - Sprints
- Tuesday - Sprints
- Thursday - Sprints
- Saturday - Long run
This will give your body time to recover and cope with the new stress of running.
There is an argument that running clubs can be handy for motivation, but motivation is mostly an interalised concept. If you want to achieve your goal, you really need to want it. Tracking your runs and weight, will help reenforce your behaviour and build a good habit to ensure that your training is consist, even on rest days.