I did not know exactly what you meant by toothpaste dots, so I googled it. Two of the first three listings explained how to make your own:
Are you not quite ready to use Dr. Bronner's soap for toothpaste? Do you have a favorite brand or need a special one for sensitive teeth? Consider making toothpaste 'dots' by drying little dabs on your dehydrator while you're dehydrating some food for your next trip. If you don't want to run the dehydrator, just put some dots on plastic wrap on a paper plate on your dashboard. To use, just moisten. --submitted by Rosaleen Sullivan
Tooth paste is squirted out on a plate, in little dabs. I leave the plate in a corner out of the way, and in a few days I have tiny nuggets of hard toothpaste. Please note: I live at 6,100 feet in idaho, it is VERY dry. These gummy "dots" are packaged in a tiny ziploc baggie, and i chew 'em like gum before brushing. Easy!