Try doing a search on eBay. I just did that and got a few pictures of vintage machines. Some might be close enough to yours to give you at least an approximate series for the model.
I think this one on eBay looks very close:
http://cgi.ebay.com/BROTHER-VINTAGE-...item336499385e
The "portable" version like this one may have a slightly different model number from the cabinet version you have.
Anything on the badge on top of the motor?