I didn't see any Veronica in Queensland or around Sydney. The first I saw was the introduced V. arvensis in Bega, a small New South Wales town. Australia has many of the same weedy speedwells that New Zealand does, so I was more interested to see plants of the indigenous species.
|Mallacoota inlet, Vic.|
|Veronica plebeia, Mallacoota, Vic.|
The flower below was photographed on a cultivated plant in New Zealand, where V. plebeia is widespread and considered by some botanists to be native. It is introduced and weedy in some other parts of the world though, so it does have the ability to be invasive.
|Veronica plebeia, from a cultivated plant in New Zealand.|
|Veronica gracilis, cultivated near Ballarat, Vic.|
Australia has 23 native species of Veronica, classified in section Labiatoides, and they are the sister group to the large New Zealand clade (section Hebe) that includes the hebes and their relatives (Albach & Briggs 2012). Thus, although they look much more like northern speedwells than New Zealand hebes, they are known to be more closely related to the hebes. And because of that fact, it's misleading to classify them as Veronica unless you classify our hebes in Veronica as well.
Albach, D; Briggs, BG. 2012. Phylogenetic analysis of Australian species of Veronica (V. section Labiatoides; Plantaginaceae). Australian Systematic Botany, 2012, 25, 353–363