Q: I barely make traditional phone calls or text messages, what with VoIP and over the top text services such as iMessage. Are there any plans which don't include calls, so I'm not paying for something I'm not using?
A: It depends on how much data you use. If you use a gigabyte or two a month, sure, if it's more than maybe 3-4GB a month, then keep an eye on the unlimited calls plans anyway, they're basically thrown in for free at that price point.
I'll assume in this case that calls and text messages are still able to be made at pay as you go rates (so I won't be suggesting pure mobile broadband plans).
Telstra: If you're happy with the wholesale network, you've got the CMobile Blue plans or the Aldi data packs (Aldi offers 4G). If you need full Telstra coverage, your choices are prepaid Simplicity or Long Life with data packs, or just going for prepaid Freedom Plus.
Optus: Check out Amaysim's pay as you go service and add a data pack. Call rates are fairly cheap, and you can buy a 10GB data pack that lasts 365 days (among others).
Vodafone: CMobile have a couple of data-only plans that charge calls as you go, and you can add data to a Lebara PAYG plan. Alternatively, you can use Vodafone prepaid, and add data plans as needed. Vodafone data packs with a 28 day expiry range from $5 for 500MB to $15 for 2GB, and they have other 2GB data packs with a shorter expiry ($7 for 2GB with a 7 day expiry and $3 for 2GB with a 1 day expiry). Although, if you're a light user, Vodafone charges 2c/MB for their PAYG data (although not on their 365 day offer, that's $2/MB).
The other option if you have a dual-SIM phone is to have a mobile broadband SIM in one slot and a cheap PAYG phone SIM in the other. This may or may not be allowed by your carrier (they may restrict the SIMs to modems/tablets), and as most dual-SIM phones have one slot operating on 3G/4G and the other in 2G, it won't work anymore when the 2G networks are all turned off. Extra complication and all of that.