I googled this plant as I had never heard of it. However, it very much resembles Convolvulus so I wonder if there has been a name change.

This is what I read:

This
is an evergreen herbaceous perennial in the warmest parts of our
region. Where it is not reliably perennial, it serves well as a summer
annual that produces large numbers of true blue flowers throughout the
growing season. The small flowers resemble those of its relative, the
morning glory. The plant grows to about a foot tall and spreads a few
feet wide with stems that root as they grow along the ground. It grows
and flowers best in a moist, well-drained site in full sun. It does not
tolerate prolonged drought or continuously wet soil. It is reported to
be moderately salt tolerant. Most references list it as a reliable
perennial in zone 9 and south.

This species is commonly available in the nursery trade. Plants
are propagated easily by cuttings. They may be propagated by seeds,
too. Recently, a plant named 'Blue My Mind' showed up in the nursery
trade. It is described as a hybrid but resembles a compact version of E. glomeratus with darker blue flowers.

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I suggest that you plant it in the garden in a position that suits it well (and where you would like to have it grow) and then wait. There will come a time when you can dig up pieces of it that have rooted.

Alternatively, if you want to grow it from cuttings, choose the tips of the new growth in very early Spring. If it's Convolvulus in disguise, it will readily root.

Convolvulus can take very rough treatment when it comes to trimming them. In other words, sometimes I get fed up with mine and give them a severe haircut, not really caring if they survive or not. They always survive. And they look a lot nicer. (Mind you, the other day I got a bit over-zealous and pulled one up by the roots. I doubt he'll put up with that. But I have other plans for that area.)

The description of stems taking root where they touch the ground says this plant ground-layers itself. You can speed the process by purposely bending branches to the ground and laying a rock or brick over the spot where they make contact with the ground. Works best if it's a spot of bare soil, not mulched or grassy. Can also bend stems to the soil surface of another pot and pin/brick it down there, being careful not to crimp the stem where it crosses the rim of the pot.

For what it's worth, Evolvulus 'USEVO1201' (a.k.a. Blue My Mind dwarf morning glory) is a patented plant and cannot be legally vegetatively propagated, without permission from the patent holder, for ANY reason (including personal use).

EDIT - I just realize that RRoss is in Australia, so the above info very well may not apply. It would here in the US.