Most phones (including the Desire I think) don´t fully support the 3G bands here. Just the 2G. So you might not always get the optimal speed (but on the other side, 3G here is not what I am used to from my home country either).
If you don´t get any data connection at all, you have to add the APN settings for your provider. Also make sure you actually have a data plan or it will cost you a lot or your prepaid credit will be used up within minutes. Personal telecom offers an internet package for prepaid for 19 pesos per week (activate it sending "act im7" to the number 152, don´t forget to deactivate data or renew before the week (168hs to be exact) runs out).
If you are using an Android phone like the HTC Desire, use APNdroid for deactivating data.
Also there is a bunch of programs to track the phone after it is stolen. Don´t expect to recover it using them, nevertheless it might be interesting to see where it ends up. Since there are not many Android smartphones in the Argentine market right now, chorros probably won´t know how to remove the programs. And yes, take care. I put my phone in the breast-pocket of my coat because it seems the safest place for me. Even saved somebody´s life once, when a phone placed in a shirt´s breast pocket slowed down a bullet that would have otherwise entered his heart. Not in BsAs though, but in almost-heavenly-secure Austria
Apart from that, I have to say that I am taking all precautions I can. I mostly use the phone at home and in closed places, preferingly sitting with a wall behind my back. Nevertheless, a phone is not worth anything if you don´t use it, so you can´t always be in perfectly safe conditions. From my discussions with Argentines, I think somebody steals or robs your phone every 12-24 months in average. For me that means:
1.) I use no phone that is like "really expensive" for me. I use a 18-month old T-Mobile G1 which I want to replace when coming back from Argentina anyway.
2.) I have a second phone (which is small and cheap) which I take with me when going out, or in other situations where it seems appropriate to me.
PS: Forgot to add: The bands of phones like the HTC Desire generally differ depending on where you buy it. I had the EU-version in mind when saying that it might not support all bands here. Don´t know what they sell in Australia or what bands are common there.
Other PS: Apps I can recommend on Android:
-Waze (navigation app)
-Transito Buenos Aires (state of subways and streets)
-Truco (a typical argentine card game)
And my last PS:
You can´t buy Android apps in Argentina (only access those that are free). You can put an Australian chip in your phone though (make sure that data-roaming is deactivated or you will be a poor man), and access the market via WiFi. This way you get access to the Australian version of the market.