Having a business plan is not "over-analyzing stuff."
If your goal with this project is to make money (i.e., it's not just a hobby), then figuring out how to monetize it is an important step.
The question you need to be asking yourself is: what value are you creating, and for whom? If your idea doesn't provide value to a group of people, it's not going anywhere as a business.
(Note that the users of the product aren't necessarily the same people it provides value for.)
If your goal with this project is to make money (i.e., it's not just a hobby), then figuring out how to monetize it is an important step.
The question you need to be asking yourself is: what value are you creating, and for whom? If your idea doesn't provide value to a group of people, it's not going anywhere as a business.
(Note that the users of the product aren't necessarily the same people it provides value for.)