The special election can’t be on April 9. According to a state law, Gov. Quinn must announce the election dates within five days after the resignation. The general election must be held no more than 115 days after the day that Quinn makes the announcement. The latest possible day for the special general election is March 21.
I don’t think there there can officially be a vacancy for the new term until it starts in January (the third I believe).
April 9th is only 96 days after that if I count right.