In reply to GrantB:
Though it's a Victorian Site and forum, there are quite a few SA members on Chockstone.org.
Local crags are in the Adelaide hills. Morialta Gorge and Norton Summit are the main two.
http://www.climb.org.au/index.php?page=25®ion_id=41
Guide to Norton Summit and bouldering at the Bachelor Pad
http://www.climbingclubsouthaustralia.asn.au/guides.html
SA's main cliff is Moonarie, but it's a long drive and quite remote so you will need to organise a partner before you go, though Feb / March is super hot so will find it hard to muster someone to go out there.
http://www.climb.org.au/index.php?page=25®ion_id=11
One of the few places in Australia which a lone traveler should find a partner is Mt Arapiles in Victoria which is I believe 4-5 hours drive from Adelaide. Also hot this time but by keeping to the shadier gullies and climbing either side of a midday siesta climbing is still possible.
http://www.chockstone.org/Arapiles/Arapiles.htm
Travelling in Australia to climb differs from places in Europe as there is a far greater pool of climbers on holiday at the same time to climb with over there rather than in Australia. The States I've also travelled solo and on only a few occassions had an enforced rest day due to not meeting up with others during a week day.
I've always travelled with a full kit. Possible if meeting some friendly local climbers who have their own gear you could just get by with shoes, harness, chalkbag and belay device.