When writing "American Dollar," should the d in dollar be capitalized?
No, it does not have to be capitalized. The following is much more common, and also correct:
There are times when capitalization is helpful, such as in long lists. But it is never required.
Another thing to Keep in mind is That Excessive or unfounded Capitalization in normal writing tends to Look illiterate, unless it's wielded by an expert artist, or by earlier authors. So I would recommend that you use "dollar" rather than "Dollar" in almost all cases.
As with all nouns, one significant use of "dollar" where it should be capitalized is in a header or title, e.g:
The American Dollar Falls Below the Canadian Dollar!