We go to Millinneum Park Dentistry w/Dr Stephen Gordon downtown Chicago across from Millinneum Park. He's not a pediatric dentist, but a holistic dentist and could possibly use ozone therapy instead of filling her tooth. His office is open by appointment only and consists of himself, a nurse, and a receptionist.
He works on my daughters - one of them since she was just a few months old (she had enamel problems.) He's not an advocate of putting kids under anesthesia or holding them down, and will even let you sit in the chair and hold her if necessary/wanted, and is extremely patient and non-threatening. They can show her exactly what they are going to do, etc. and have no problem taking their time.
He uses fillings that don't contain mercury too, so if they DO break, there's no the danger that is posed with other dentists' fillings. They have headphones so she could listen to music if she wants (or you could take your own iPod or whatnot) and sunglasses so the light doesn't glare into your eyes.
I wish you the best!