The OHIP waiting time is for everybody moving to Ontario. You did not move to Ontario in June 2011 because you only stayed for a month, like a vacation. OHIP also has certain rules like to qualify for OHIP, you must stay for 5 months out of the first 6 months you are there and also that you must in general stay for at least 6 months a year to keep your OHIP.
Of course it is possible for you if you do not want to pay for the delivery of the baby to choose another province with first day coverage such as Alberta, Saskatchewan or Manitoba but be aware that if you do, you should stay there for at least 6 months because otherwise you break the 6 months a year rule and they might just decide retroactively that you shouldn't have had coverage and decide to charge you for it.
The 3 months start on the day you take up residence. If you want to live in Ontario, you can apply for the health card before you qualify but you will not get it until your 3 months waiting period is over. If you move back in January 2012, you will qualify for your health card in April.
To keep your health card, you can only leave for a month during your first 6 months there and after that you must stay at least 6 months a year.
I think it is about your posted bank statement and utilities bills. if you have them means you'r staying in there.Anyway I was told if you apply for health card in the first visit, which wasn't easy, you will have health insurance valid by next visit let it be after a year. One trick to apply for health insurance in the first visit is to apply for a bank account and a photo card once you landed there, when you get them by post say after 4 weeks then you apply for health card and you will get it by post