Kerr’s side need a two-goal win over group leaders Switzerland next Thursday, 30 August, in Paisley, followed by victory in Albania five days later, to secure an automatic place at the finals in France next summer.
“The women’s team are on the cusp of something special, being one or two games away hopefully from a World Cup,” Kirk told BBC Scotland.
“There’s a strong influence now in the WSL [England’s Women’s Super League] in terms of Scottish players; Shelley can easily put a team out now that are based in England.
“I suppose there’s a little bit of pressure because you want to continue that positivity in terms of strong Scottish influence in England.”
Kirk admits it was a “proud moment” for him personally as former Hibernian duo Arnot and defender Kirsty Smith both signed their first full-time professional contracts with the Red Devils in July.
Arnot, 22, has come back from a year out – missing the European Championship finals last summer, Scotland’s first major tournament – following a cruciate ligament injury, and scored five goals for Hibs in the Scottish Women’s Premier League Cup final before moving south.