A DateTime
can accept input in its constructor with an alternative calendar, but internally it is always stored using the Gregorian equivalent. So you already have what you are looking for.
Calendar umAlQura = new UmAlQuraCalendar();
DateTime dt = new DateTime(1434, 11, 23, umAlQura);
// As a string, it will format with whatever the calendar for the culture is.
Debug.WriteLine(dt.ToString("d", CultureInfo.InvariantCulture)); // 09/29/2013
Debug.WriteLine(dt.ToString("d", new CultureInfo("ar-SA"))); // 23/11/34
// But the individual integer properties are always Gregorian
Debug.WriteLine(dt.Year); // 2013
Debug.WriteLine(dt.Month); // 9
Debug.WriteLine(dt.Day); // 29
Going the other direction, you have to get the parts using the methods on the calendar object.
DateTime dt = new DateTime(2013, 9, 29); // Gregorian
Calendar umAlQura = new UmAlQuraCalendar();
Debug.WriteLine(umAlQura.GetYear(dt)); // 1434
Debug.WriteLine(umAlQura.GetMonth(dt)); // 11
Debug.WriteLine(umAlQura.GetDayOfMonth(dt)); // 23
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