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Yes, set the dates on the existing one to 4/1/2011 and 4/30/2011, repeat every year, check it off as completed, and check the result. You'll be able to see it in views showing remaining actions, but it will be excluded from views showing available actions until April.

Tip: you can experiment with this stuff by bringing up the inspector and using it to enter specific completion dates so you can see what gets created. Not as useful with repeat every as with start again and due again as repeat every's behavior doesn't depend on the completion date, though.