Polka, that sounds like a good plan.
There are lots of 10k training plans on the web, just pick one you like. The beginner ones are aimed at someone who has never done that distance before, so you probably want an intermediate one or " improve your 10k "
If you start from the base of being able to run 10k, you can use your 8 or 10 week training to improve your speed and endurance. As a general guide, to be properly prepared and get a good time for a 10k you should be running at least 3 times race distance -so for you that's 30k per week, including a long run or 10k or more. Once you are doing a15 k each week, the 10 k will feel easy !
Your plan will also have some cross training and some strength work .
It's good to allow slightly longer than you think you need for training. Then you can have time off for a holiday, injury, illness ( yours or kids ) etc. Lots of runners don't do this, then when they get an injury they run on it rather than rest, because they only have a few weeks left before the race. Or they panic because the kids are poorLy and they can't run for a week. Or they don't allow enough time to taper ( cut down for a period before the race ) .
So I'd start a 10 week training plan 11 weeks before, so that's in a few weeks if your race is in early September.
That's just me, I'm very cautious and always stick to the plan. Lots of others here are more free spirits with regards to training 
and just do their own thing .