Yes. The tooth is destroyed and irreparable. If you don't have it fixed right it will eventually turn dark and rot away in her mouth.
Please go to a pediatric dentist.
All dentists go to a medical school for dentistry. Much like a regular doc. They do short terms in each area such as braces, pediatrics, family, and oral surgery. They do this so that the docs get a small taste of each area and can make sure the area they want to go into is the right one for them.
A pediatric dentist will usually start seeing kids as soon as they're born. Sometimes there are problems that need a dentist to be addressed. These pediatric dentists generally have a completely different approach to dealing with their patients. They might have stuffed animals for the kids to play dentist with while they're getting their teeth cleaned, they might have toys and TV's in the rooms too.
They specialize in tiny toddler age children. Our pediatric dentist sees kids up to age 18 then they have to find a regular dentist.
One thing that pediatric dentists do is put the kids to sleep while they work on them. Ours uses Children's Hospital Out Patient Surgery for his asleep dental work. He has a trusted anesthesiologist that he always uses. She is very very good at treating very young children. Some will treat the kids in their offices but they use a liquid to put the kids out, awake sedation, and they get all the work done in a few minutes and it's over.
This tooth is gone. You have to accept that. I didn't believe the dentist when my daughter fell off the couch onto her bottle and busted her front tooth. He wanted to do a root canal and cap it. I said no, she was too little. Her tooth rotted and smelled and looked horrible. It finally fell out and her other teeth moved to fill in the hole. When her adult teeth started coming in they didn't have the right spacing to grow into and her whole smile was messed up.
If you really don't want to do the root canal seek another pediatric dentists opinion.
My granddaughter fell up a flight of concrete steps and broke her front tooth off. That's how we found our pediatric dentist. He did her tooth in about half an hour and when it finally came out I couldn't tell where the tooth stopped and where the cap started. The dentist was that good. Only put white caps/fillings on the teeth in the front. Kids have a hard enough time without giving them a big reason to tease someone.
My grandson had a cavity we couldn't see. When we took him in the first time the doc said it had to be capped. Since it was a jaw tooth they used silver.