The best time to visit Kangaroo Island is between November and March (though you'll have difficulty finding lodging over the Christmas school-holiday period). July and August tend to be rainy, and winter can be cold (though often milder than on the mainland around Adelaide). Many companies offer 1-day trips to Kangaroo Island from Adelaide, but I would advise you to tailor your holiday to spend at least 2 days here -- 3 or even 5 days would be even better.
Note: This information was accurate when it was published, but can change without notice. Please be sure to confirm all rates and details directly with the companies in question before planning your trip.