My kids have needed the electrically powered nebulizer where you put the vials into the base of the piece that covers the mouth. But they've since been moved to using the "puff" type nebulizers which deliver the dosage in an an inhale-able "shot" through the mouthpiece. No electric pump/unit to carry around.

Your child's condition may warrant something more like the powered unit, but it's worth asking the doctor if you can use the 'puff' type unit that is easily carried in a purse or small bag (and isn't electric).