Allen is an awfully common name. Sellers (American Gunsmiths) lists two of them in New York, both in about the right period. I don't use Sellers much because his work appears to be just a compendium of all the previous lists, copied without much regard for verification. Thus, while lots of it is good, everyone's earlier mistakes have been incorporated as well.
That said, I don't think it was made here. It has all the look of a Birmingham export product, retailed in New York. It is, however, quite early for a percussion gun. Those hammers with the wide flat face seem to date in the mid to late 1820s, perhaps as late as 1830. Its quite unusual to be able to date guns like this in anything less than a 20 year bracket but I've seen a few now that can be given a terminal date (because someone died or went out of business) and they all seem to fall into this time frame.