You can normally claim EI up to 8 weeks before your due date, but if you only started paying into EI for self-employment last June then you're right, you wouldn't be able to claim it until June, since you have to pay for a full year to qualify. Although, it would be worth calling and checking into short-term disability. I don't know if you can get that just by paying into the EI program, and I don't know if the year's waiting period is the same, but it couldn't hurt to call and ask.