The Islamic calendar is lunar calendar. A year consists of 12 lunar months of 29 or 30 days each, so it ends up being shorter than a solar year by about 10 or 11 days. Since lunar calendars don't lend themselves to agricultural uses, people in Muslim lands have almost always used other calendars alongside the Hijri (Islamic) dating system. I would assume that her age was reckoned in lunar years. They're similar enough in length to solar years that her reported ages (6 or 7; 9) would be approximately the same under either dating system.

Was this actually the case, did Mohammed actually marry a 6 year old girl and consumate at 9

The answer depends on your view of hadith evidence, which is the source of this information. These ages are reported in hadith collections that are generally considered authoritative by Sunnis. We know that a lot of the hadith literature is apocryphal—Muslim hadith scholars themselves recognized as much—but some of the information it transmits is bound to be authentic. Personally, I think that the ages are plausible. Young brides have been common throughout history. I don't think there's evidence of anyone being scandalized by 'Aishah's age before the 20th century or so, and none of Muhammad's ﷺ contemporaries seems to have regarded it as unusual.

Some scholars and apologists have argued against the accuracy of these ages. One argument relies on indirect evidence from other hadiths, from which it can supposedly be deduced that her age was closer to 17 or 20. Another argument suggests that tradition has artificially lowered her age in order to emphasize her virginity and purity. Whatever the case, to get back to your question, her age has not been distorted by conversion between calendars.

For a brief overview of Islamic calendars, check out pages 20-22 of Marshall Hodgson's The Venture of Islam, vol. 1.

For a version of the hadith in question, see http://sunnah.com/bukhari/67/70

Edit: poor wording