Hi Coleen,
You would currently be entitled to FIS as you are working 20 hours pw, but as the min weekly hours are 19 your entitlement would end when your current role ends as you are expected to advise FIS section if your hours of employment changes. If your assessable income (take home pay plus lone parents allowance) is less than the limit, ie for one child €506 per week you will have an entitlement to FIS payment, being 60% of the difference between you income and the income limit for your family size.
Apparantly the current wait time for new applicants is very short, just a number of weeks (thought there is still a backlog for applicants sent in prior to November of last year)
I'd recommend you get your application in as soon as possible, you can download forms from Dept of Social Protection website. You will need P60 from last year and some payslips as well as having the form signed and stamped by your Employer.
Good luck