When you become a bit more advanced at playing didgeridoo, you may want to introduce a few other things just to spice up your playing a bit. If you play something else, try playing your other instrument at the same time and see how it sounds.
If you don't play another instrument, you could introduce some simple percussive elements. Because the didgeridoo is more like a percussion instrument, I believe they are best suited to playing with other percussion instruments. Didgeridoos are probably best known for being played with drums or djembes.
If learning the drums is a little too advanced for you, just try playing with simple clap sticks and or a shaker. Learning to play didgeridoo with these things will help your playing immensely. Firstly, it adds another sound to your playing. This will help your didgeridoo playing sound a little more layered and interesting. This is useful in contributing to the mood of your playing and keeping the audience engaged.
Secondly, clapping or shaking in time will really help with with your sense of rhythm. It will make you concentrate on staying in rhythm more. When you have a good sense of rhythm, your playing sounds more professional and you are less likely to stumble as you play your solo.
Also, having a good sense of rhythm makes your playing sound like it has purpose and a sense of movement and direction. This will make your solos sound more professional and once again, your audience will be entertained for longer.

Clap sticks and shakers are a good accompaniment to the didgeridoo.
For the adventurous type, you can even combine these and add two extra sounds to your didgeridoo playing, without needing an extra hand! Simply tape an egg shaker to the end of your clap stick and you have a nice improvised percussion instrument with two distinct sounds.
Hit the sticks together and you have a strong clap and shake sound. Shake the stick by itself and you have a rhythmic shaker sound. The two sounds can easily be combined to make a great accompaniment to your didgeridoo playing by hitting on main parts of the beat and shaking during other times.

An improvised clap stick and shaker combination.
If you are wondering how to do all this and play didgeridoo at the same time, the clap stick can be easily held by the hand that supports the didgeridoo. Just use your index finger to keep the clap stick away from the didge. Strike this clap stick with the other in your free hand.

A simple way to hold your clap stick and didgeridoo.
If you need help holding all of these things or you are thinking about playing another instrument at the same time, a didgeridoo stand is a good accessory to have, although not hugely important unless you are starting to play gigs. This will free up your hands so you can use your clap sticks or shakers and play at the same time. Fun!

A didgeridoo stand.
Being a rhythm instrument, didgeridoos go well with other rhythm instruments, like drums or clap sticks.
Simply adding the sound of a clap stick or shaker can introduce an exciting new sound to your didgeridoo playing. This will make your playing sound more rich and layered.
Tapping in time with a clap stick or shaker, although difficult at first, will really help you with your sense of timing.
You can use a clap stick while holding your didgeridoo, or if you want to free your hands up, use a custom didgeridoo stand.