there are so many moving parts involved that any answer given here will be just a wild guess or someone else's experience which may not be applicable to you.
First things first - you assume you will have your ppl by September - which is a very realistic objective as long as the school has planes and instructors available and you are equipped with the right attitude/aptitude and cash. Should you pick a small school with only 2 - 3 planes, or perhaps a larger school that's very popular meaning it might be difficult to get the slots you need - your plan might come apart right there and then.
Once you have your PPL, for the ATPL you need to study for about 2-3 hours a day on average for about 3 months per module, at least that's the rate I'm doing it right now. If you only work 4 days a week, you might do it quicker. Again this is one of those things where the next guy will come and tell you he did all 14 subjects in 2 months followed by the next guy who will call him a liar and try to convince you that ATPLs are the hardest thing in the world and it will take you 2 years to get them done.
To be honest, I wouldn't worry too much about the timelines at your stage. Go chase that ppl first and figure out whether you even like flying or not. Statistically speaking the odds are you will drop the whole aviation thing just after your first solo