I don't know the name, but maybe this site could help:http://www.missingfabrics.com/
I think you post scans of fabric and ask if anyone is willing to sell some. In the process you might also find out its designer and brand.
Will put my thinking cap on, but right off the bat I'd guess a 1930's feedsack reproduction print
I would search Windham fabrics - their Storybook lines (I-IV and Moda- their 1930 reproduction lines...hope that isn't a wild goose chase but the dots resemble the "boll dots" in Windham's new line called Once Upon a Storybook...there are several other feedsack lines as well...not sure of all the makers:)
I found two fabrics that are close (but not exact):
I'm still looking, though... I love a good scavenger hunt! :)