Hey A.,
I am a RN. I work critical care ER/ ICU. I will tell you I've given Versed hundreds of times for procedures ranging from putting a cast on to setting up a patient to go on ventilator. It is used VERY commonly. Yes there are side affects, you do risk respiratory depression, but anyone who has experience giving it knows how to properly handle the risks. I am assuming your dentist is specialized in pediatrics. That would leave me feeling more comfortable. Pedi doses of medications are significantly smaller than adult doses according to your child's weight. If you are uneasy.... ask the staff.
However, know that it is a short acting drug, and if she does get too far under (suppressing her respirations) that there is medicine they can give to reverse that. I'd be sure of a few things. Make sure they have a way to monitor her oxygen saturation, vitals (pulse, blood pressure, etc)and have an ambu bag at the bedside should she need supplemental oxygen temporarily. They should be able to assess her status with all of the above mentioned equipment.
Be prepared that they may not let you back in the room with her while she's out. Depends on the facility's policy. Do know that she'll not remember thing one about the experience. Versed is a dissociative drug that suppresses the central nervous system of the brain temporarily. When you come back in the room she will seem spacey and may not entirely remember who you are. Kinda like she kicked back one too many ;). That is ok.... she'll be sleepy a good chunk of the day and the immediate "forgetfulness" should wear off within an hour or so of her procedure. If there is anything else I can help you better understand or ease fears, don't hessitate to write me back. I'd be happy to help you out! Best wishes, I'll keep her in my prayers.