A hat is a good idea, yes. I like them both for the extra protection during travel, and to put on my drum during breaks at workshops, to guard against coffee spills and such.
Here is a shot of tools that permanently live in my djembe bag:

- Useful tools
- IMG_4525.JPG (102.21 KiB) Viewed 418 times
The rope puller and pliers are for tuning. The drum key is needed for my drum throne, which has a stupid design with a stop that requires a key. If I ever buy another stool, it'll be a design that doesn't require tools.
The thing on the left is the end of a deer antler. That's a phenomenally useful tool. It works as a wedge, to lift off the vertical from the side of the shell when weaving, to reduce wear on the rope. It also is awesome for poking open knots, or to lever tensioned rope away from the drum when stowing the end of the rope. It's soft enough not to dent or scratch the wood, yet strong enough to get serious leverage. If you can, find yourself one of these—mine is one of the most often used tools in my workshop.
Another thing I found useful is a clip-on handle:

- Djembe handle
- IMG_4527.JPG (131.44 KiB) Viewed 418 times
I used to put these in "unnecessary" category, especially the ones with plastic hardware. But, since coming across models with decent metal hardware, I've changed my mind. They are easy to clip on and remove, and I can move a handle between drums in seconds. Less work than making my own that's permanently attached to the verticals, and they are available in all sorts of nifty colors.
Cheers,
Michi.