There are a number of third-party apps available in the Android and Apple app stores that could work with your Moodle site, including one that works with Moodle 1.9:
mTouch: This app is available for Apple iPhone, iPod Touch, and iPad only, and supports iOS 4.3 and above. It is for students' use only. It costs a couple of dollars to download and is under active development. It is available at http://www.pragmasql.com/moodletouch/home.aspx.
MoodleEZ (MoodleEasy): This app is available for iPad only, and supports iOS 4.3 and above. It is from the same makers as mTouch. It can be used used by students, teachers, and administrators. It costs a couple of dollars to download and is under active development. It is available at https://itunes.apple.com/gb/app/moodlez/id449138373?mt=8.
iActive (previously mPage): This app is available for iPhone, iPod Touch, and iPad, and supports iOS 4.3 and above. It works with Moodle 1.9 and above, and seems quite fully featured in its...