What is this type of dress called that the peasants would wear during Old English eras, along with a bonnet?

Your question makes no sense, because in the "Old English" era, i.e. c400-1100 AD, the bonnet hadn't been invented. Highland soldiers started to wear the flat blue "Scots bonnet" in the 15th century; that was the earliest bonnet to be worn by common people in Britain. "Bonnets" in the sense "outdoor headgear for women" weren't worn till the 19th century.