If the "father" does not qualify for guardianship, how soon can her apply for guardianship and does he have to meet certain criteria to obtain even limited guardianship?

Who has the kid(s) now?
Why were (you?) father denied guardianship?

And why is the word "father" in quotes?

I have the child now. According to the Family Law Act, her "father" is not considered to be one of her guardians. He has to apply for it. I just wanted to know if he had to meet certain criteria before he would even be considered one.

Who are you in relation to the child? And again, why are you using the word "father" in what appears to be a qualified sense? Are you sure you're understanding this "Family Law Act" correctly? I've never heard of a legal father having to apply for "guardianship." Custody, maybe, but that's different. If the father wants any kind of custody, be it sole or joint, physical, legal or both, he can file a motion with Family Court. Generally it's up to the judge who'll make a decision, based on a combination of statutory and case law, relative to the best interests of the child. But he doesn't need to meet any special qualifications or "criteria" to be granted anything. Now if he's demonstratively an unfit father (history of child molestation, incarcerated, habitual drug use, etc.) then his options will be more limited. But he can still bring the matter in front of a judge.

I think you are saying that he has to file for joint custody/visitation and he hasn't done that yet. Yes he has to file otherwise the courts aren't going to know he wants to have any part of the child's life.
You will have to explain the situation better if that isn't what you are asking.

If the "father" does not qualify for guardianship, how soon can her apply for guardianship and does he have to meet certain criteria to obtain even limited guardianship?

Where is this at ? It sounds like Ireland ?