First of all: congratulations on getting hired! Sure, the first job is always scary (frankly, I consider every single one of them to be a bit scary), but it'll (hopefully) also be a lot of fun and very insightful.
For as far as I can see, you're totally on the right track! The outline is very important, as you'll have to properly communicate your vision with the client before you start shooting. The schedule is a good idea as well: make sure your client and you know when you'll be working for them and what you're going to do on any particular day. Be flexible, though, as the client (who I believe the documentary will be about) does have a life of his/her own. You don't want to be a big pain in the ... during production.
At the same time, make sure you stay on schedule and if you run into any problems, communicate them clearly and ALWAYS have a solution ready. For instance, on one of my shoots, something went wrong with the audio recording and I didn't notice for weeks. When I told my clients that some of the early footage was practically useless, I did immediately propose to change the project ever so slightly, so we wouldn't need to use the audio of those clips. Sure, the client didn't like the message, but because I was able to say "but we could do this...", they weren't pissed off at me either.
As to how much you should charge: that's a tough one, but do make sure you turn a small profit. You (probably?) don't have to make a living off of it yet, so don't go too crazy either. I do charge based on the amount of time I spent working on something, not on the type of project it is. If I work on something for 20 hours, I'll charge 20 hours (just an example).
If you have to rent equipment, always add that to the price. Those are costs and the client has to pay them, simple as that. Also, try to get insurance on that equipment, because if you drop it, you break a couple of thousand bucks worth of equipment and you don't want to have to deal with that mess (in Europe, oftentimes the rental house will take care of insurance, don't know how that works in the rest of the world). Stay reasonable with rentals, though. If you can shoot it on a 5D, don't rent an FS7. Do make it look professional, though, because this project will be the only piece in your portfolio for now.
So, you're doing great! If you keep planning ahead, keep communicating with your clients in a way that they understand (not everyone's very tech-savvy) and stick to your deadlines and budget, you'll be fine.
Good luck and have fun!