I breastfed for 3 years. I also needed a root canal as a toddler. Breastfeeding isn't a cure-all for oral health.
Do you brush your teeth with your child? That works for kiddo. Your toddler should be around the age of "I want to do everything my parents do", which is a really useful age for getting them to do things like brushing their teeth.
I brush my teeth, then kiddo grabs for the tooth brush, I get down to his level and let him grab it (I keep a hand on it for guidance), let him guide it to his mouth, get comfy with it. Because your toddler has such a problem with toothbrushing, you may want to do that a few times before trying to actually brush the teeth to get her a little more comfy with it. Yes, toothbrushing is important, but a few days to get her comfortable with it is a LOT less damaging to oral health than a lifetime of hating to brush your teeth. I know someone with a 9 year old who she still has to fight with on toothbrushing!
Once he has the brush, I do as much as he'll let me. Then I'll brush my teeth again and he'll usually grab for the brush again, and we repeat. If he gets bored before I think we've done enough brushing, I'll push a little bit further- but I don't want to develop a negative association so I'm not going to go to the point where I'm holding down a screaming child and shoving a tooth brush in his mouth. A lot of adults don't have healthy teeth or good brushing habits- at some point, I'm not going to be able to physically overpower him anymore, and I don't want that to be the last day he brushes his teeth. Of course, I'm fortunate to have a baby with fabulously healthy teeth that can handle it- if he was already showing signs of bad oral health, it'd obviously be a different story.
When you brush your teeth with your child, you can use the toothbrush you want your child to use (and obviously only use a toothpaste you're okay with your kiddo having in their mouth when you do this!).
Now, for whether or not it's REALLY necessary...
I would do a lot of research on the subject of dental health and come to your own conclusions. My conclusions are very much out there and against the grain, but here they are:
It makes no @#$@# sense for an animal to evolve to need chemicals to keep their teeth alive. I know of no other animal that does. Look at all the wild animals out there who live fairly long, tooth-filled lives without toothbrushes or toothpaste. We never brushed my cats' teeth, and they lived a long (for cats) life and died with their teeth still in their mouths. It makes far more sense that a truly healthy diet will produce strong teeth that can rebuild themselves and heal a fair amount of damage.
Now, animals do have ways of cleaning their teeth- but they don't involve brushes. There are some especially crunchy people who chew on a certain kind of branch known to have beneficial properties for teeth instead of brushing- basically what our toddlers do while teething. (look up whether or not that branch, or any other, are safe for toddlers before attempting to let your child try it, personally I don't) Honestly, I think part of the chewing instinct of teething isn't just help with the pain- it also used to be how we kept our teeth clean.
There's evidence of primitive societies with healthy teeth, of the modern diet leading to bad oral health in a single generation, anecdotal evidence of people healing cavities, etc. But, I admit, this was mostly just hypothesis and ideology until my toddler's tooth healed itself. He had chipped half of his front tooth off, now it's almost regained its full length. (he chipped it about 3 months ago) A tooth that can do that can surely handle a hole, so I'm not as worried about cavities as I would be. This experience combined with the number of people I've heard from who healed their own cavities makes it much easier to have faith in my toddler's body to do what it should and relax about tooth brushing.
Now, what "a truly healthy diet" means is up for debate. No one knows, and it likely varies person to person. I don't even know if my toddler has one. Also, some people are just genetically lucky (won't get cavities even if they eat nothing but sugar) and some are just genetically unlucky (get cavities just by thinking about sugar). One thing we sometimes forget in natural circles is that it used to be that a lot of people died without modern interventions- now those people live and pass on their genes. Natural toothpaste doesn't work for my partner, even though it works better for me. My partner is one of those people who does need to brush their teeth with the modern toothpaste, and our baby shares genetics so may as well. This is why tooth brushing is still very valuable, because you just don't know. Brushing your baby's teeth is insurance. If you could say with 100% convinction that your toddler had great genes and a diet that would prevent cavities (or allow any that form to heal before they get too bad)- that'd be one thing, but how many people can truly do that? I certainly can't. I had a healthy diet and still got serious cavities, after all.
HOWEVER: I know a lot of people on this site don't use store-bought baby food, but have you ever read the labels in the baby food section? Sugar. Loads of sugar. Too much #$@# sugar. I'm not even talking toddler food, I'm talking baby food. Food designed for babies under a year old, with added sugar in it! "Teething biscuits" with a butt-load of sugar- I actually tasted one and almost spat it out it was so sickeningly sweet! I heard someone put forth that a 9 year old today has already eaten more sugar than an average adult has in their entire lifetime. Cavities are caused by bacteria feeding on sugar. When we dump this crapload of sugar into our kids' mouths- guess what's gonna happen? So, yeah, I feel safe going out on a limb and saying that the increase of toddler cavities just might have a little something to do with the crapload of sugar we throw at them. To make matters worse, the ones with 'vegetables' in them are shameful- "apple and kale" stuff with 'kale powder' listed under "less than 1% of"! Any child that's primarily fed store-bought baby foods, especially finger foods, probably isn't getting much, if any, vegetables and is getting a ton of sugar. No wonder their teeth are crumbling.