JavaScript, unlike some other languages, does not have any direct way of getting a character from its Unicode name. In my full Unicode input utility, I have therefore used the brute force method of using the Unicode character data base as a text block and parsing it. You might find some better, more efficient and more maintainable tools, but if you need just some specific collections of characters as in the question, an ad hoc approach is better. In this case, you don’t even need the Unicode names as such; they would be just an intermediate step from dot patterns to characters.
Clause 15.11 in the Unicode Standard, chapter 15, describes the allocation principles for Braille symbols.