It's not bad to start early, but it definitely is to rush. Since, you are currently in 11th, it would be rather better to take your time and understand all the concepts of 11th clearly. In cases of JEE preparation, it is better to take it steadily and clear the concepts. As for completing before 31st August, It can be done if you give time to each subject. In 12th you won't have sufficient time to re-visit the concepts of 11th from scratch again, but if you will clear 80-90% concepts of 11th in 11th only, you get a huge advantage over most of other aspirants who rush things off.
Thinking to dash ahead to cover up the courses lefts too many holes in your preparation. so my suggestion is take your time to complete the 11th course. It doesn't matter if you take up to January or even February. You get a lot of free time in Summer vacation. If dedicated towards completing the syllabus, that would be the perfect time to Dash the course. So, it's pretty much easy to complete the course by September. Taking August as a target would just strain you, IT WON'T HELP FOR PREPARATION.
As for the plan, I would just say to attend all classes, highlight what's important, and work enough problems to be 100% confident on that. How many hours you study is not important. Everyone is different. Some can do it in 2 hours a day study, some may take up to 5-6 hours a day. Know yourself and you can figure out the best way to complete the syllabus by yourself.