If you look under Gilderoy here Gilderoy and look at the various tunes, you'll find that the 'Little Beggarman' is a variation of 'Gilderoy' found in many older publications than Bunting's. One well known variation is known as 'The Star of the County Down' and that melody (close enough) was printed by Lucy Broadwood in 1893 under 'Lazarus: from English Country Songs'. I have traced this tune family back as far as an 11th century Gregorian chant "En Gaudeat"