Definition of "unquailingly"

Emily looked across at the girl. Large, steady, purplish-grey eyes gazed into beady, twinkling, black ones—gazed unquailingly—with something in them that cowed and compelled. The black eyes wavered and fell, their owner covering her retreat with another giggle and toss of her short braid of hair.

1923, Lucy Maud Montgomery, “Chapter 8”, in Emily of New Moon