Hi S.,
We had the same struggle with both of my boys when they were that age. It's tough for them because their gums are so new and sensitive, even more so with more new teeth coming in. A few things that helped with us were praising them when they cooperated and tried to make it fun, giving them a turn first (they really like the taste of the baby toothpaste and feeling like they can do it themselves) and then telling them that it's mommy/daddy's turn, being as gentle as possible, and just having it be a part of the bedtime and morning routine so they know to expect it.
I definitely suggest getting a baby toothbrush and toothpaste. The baby toothpaste is safe to swallow, and the kids really like the taste, which helps them want to participate in getting their teeth brushed. As for the toothbrush, I suggest getting the widest head with the shortest bristles possible amongst the baby toothbrushes. The sugars are the worst for their teeth, but any food will create plaque that builds up on the teeth, which is probably what you're seeing, and you need something with bristles to get and keep it off.
I also strongly suggest taking your daughter to a pediatric dentist. It's a misconception that babies and young toddlers are too young to see a dentist, when in reality, as soon as they have teeth, they should see a dentist. Teeth need dental care, no matter how old the child is or how new the teeth are. I'm not sure what area you live in, but I really love my pediatric dentist. They really make the visit as fun as possible, and they talk to the kids and explain everything in a fun way. Here's their info if you're interested:
Kirkland Children's Dentistry
Dr. Clint Worton DDS
620 Kirkland Way
Suite 102
Kirkland, WA 98034
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Best of luck to you! :o)