Here's (what I hope is) a useful tip.
To combat the problem of uneven light in you photo, say for example where your bunny has a big fat head casting shadows over the mouf area when lit from above by your standard light bulb, you can use a reflector. A reflector, in photography terms, is a flat shiny surface you place just out of shot and angle to reflect light back at your subject. Sure, you can buy fancy purpose-made ones from camera shops or online, some of which are quite cheap, but since bunnies are quite small, you can also just use a sheet of kitchen foil stuck to a bit of card.
You can get different looks by using different coloured surfaces, a golden surface will have a warming effect etc, and in fact you can even just use a piece of paper. Neat, huh?!