Leaving job, raising child -- EI?

My wife is a teacher, and she went on maternity leave last September when our son was born. She will be returning to her contract position when school resumes next month, and I will be leaving my job to stay at home and care for the lad.

My employers had asked me (out of curiosity) if I was intending to use/take/claim EI benefits, and I hadn't thought that far ahead and was unsure how that whole thing goes. I was under the impression that one could only receive EI benefits if one was actively pursuing future employment and/or was not voluntarily leaving ones former position. They seemed to think one can receive payments for a year with no fuss. At least one of us doesn't know what they're talking about.

Please set us straight about EI, PFC. I am in Ontario. I have worked at this job full-time for five-and-a-half years. I am voluntarily leaving my job to raise an at-the-time 11-and-a-half-month-old. Has my wife already used up any of our eligible parental-related benefits in her year off? Does EI apply to me?