We switched to the fluoride when my son turned 4 -but we practiced intensively for weeks to get ready for the "big day". I still make him lean forward a lot over the sink while brushing. That way he's less likely to swallow the paste by mistake -it tends to drip down onto the sink instead. Otherwise he forgets sometimes and swallows the first mouthful (because it tastes toooo good)
We actually started practicing with sips of water only at first. Wen he had that pat down, we tried holding the non-fluoride in the mouth for a few seconds before spitting it out. It's just a matter of practicing, but at three, your daughter might be still a bit too young.Don't rush it unless she's ready for it.