Hi M.,
I'm a mother of two kids, currently work as a dental rep and use to work in a pediatric dental office. As for a brush, I HIGHLY recommend an electric toothbrush, reason being; 1)this will help them get use to the sound and vibration similar to a hand piece (cleaning instrument) used in the dental office, 2) sit on the floor with them, head in your lap, this is a great way to see inside their entire mouth - if for some reason they resist (maybe as they get older) you can gently put there arms under your legs so their not trying to fight you or pull things out of their mouth, at such an young age you don't have to use toothpaste, but if you do make sure it's non-fluoridated. You want to wait until their old enough to spit in the sink to use the regular kids toothpaste. 3) take them to the dentist with you, or sibling, cousin or friend. Let them watch you do a "great job" at your appointment, then let the hygienist let them feel on their finger what their "toothbrush" feels like and don't forget to have them give her a special toy/treat/sticker for being such good girl, always create a positive experience.
Another thought, if you want them to have fun with it, let her brush in the morning, and you brush at night (your turn), this will eventually teach her how to brush while allowing you to do the really good brush before she goes to bed. Kids don't have the dexterity to brush really well until their about 7-8 years old, and the most the important time to do that great brush is a night, before going to bed with all the stuff they have eaten or juices they may have had all day. Once they start to get their 20 baby teeth in, start flossing immediately - they have great products that help parents floss their kids teeth, so it doesn't have to be just regular floss, that's hard enough for us to use:)
Limit juices for as long as possible, even though the labels say 100% juice, it's still sugar after it's all said and done, juice, snacking on carbohydrate and going to bed with the bottle are major contributors to baby tooth decay.
I applaud your efforts to take this challenge on, some kids do great early on and some need a little help, it's never to early to brush them, even massage their gums as an infant. I have unfortunately seen too many cases of baby bottle rot, it's so sad to see these little ones go through it.
If anything, always try to create the most positive experience at the dental office, also take them to a pediatric dentist, these dentist now days are trained to handle even the most difficult children and create a great experience. How many times have we said, "we hate going to the dentist," we can change that with our kids.
Let me know if you want me to send you some kids brushes (from the company I work for) for your daughter, again I highly recommend power brushes, there the fastest and best way for us parents to get in their tiny little mouths to do an efficient job, the brush does all the work!