Green’s Dictionary of Slang

1. an unimportant person.

1922		Joyce Ulysses 713: Miss This Miss That Miss Theother lot of sparrowfarts skitting around talking about politics they know as much about as my backside.
1992		S. O’Callaghan Down by the Glenside n.p.: His assistant was a tiny, sparrow-fart of a man [BS].

2. an irritable child.

1975

E. Brady All in! All in! 2: Such a child [...] will also be called a ferret or described as ferrety-faced or have a farthing face or, most cutting of all, a little sparrow-fart.