I've not tried this yet, but have it in my mental index file. Ask her why she is afraid or what she is afraid of. If she says monsters (Vampires/witches/whatever) Make and anti-monster shield. Use on old cereal box cut to shape and the let her decorate it. She can hang it over her bed or have it next to her bed. If you want say a prayer over it. (just like the knights of old) I like this idea because it gives her the power to 'make the monsters go away'.
Another thought is a small 'candle' lamp. (Usually the kind you find around Christmas.) The bulb is generally 4watts to a max of 15 watts. I know Joanns Fabric and craft stores carry these year round(they may also have small shades to put on them). This may be a good compromize to the large lamp.
If nothing else she WILL outgrow this, eventually.