Donkeys are very curious and if raised well they are also very personable. If you are trying to photograph a donkey that does not know you it will try to get to know you, getting impossibly close to your camera. Even if the donkey knows you it will get up close and personal, looking for snacks, pats, or just saying "hello".
|She would be even closer if she was not behind the fence!|
In all seriousness if you want to take a picture of your donkey one of the best solutions is to have a friend help you. The friend can either hold the donkey on a halter and lead and keep it a reasonable distance from the camera, or they can use themselves as "donkey bait" standing just off camera but having the donkey focus on them so you can get your camera in a better position for picture taking.