20 month old determined and frustrated.?

My 20 month old is determined to do all the things her older sister does, including putting on her own boots, doing up her own jacket, and putting on her own hat (which incidentally, she can do the hat quite well). But when she encounters difficulties, she gets extremely frustrated and has fits. If we offer to help she gets even more agitated. Anybody else have this with a younger sibling and how should we deal with it? Thanks.