Acanthizids (and probably many other small Australian insectivorous birds)
appear to get most of their water from their invertebrate diet, which is
high in water content. Drinking water is also obtained from early morning
dew that is deposited on the vegetation. White-browed Scrubwrens, at least,
also eat small juicy berries (e.g. Rhagodia berries) when in abundance,
which would also provide supplementary water.
Two references you might like to look up are:
Ambrose, S. J. & Bradshaw, S. D. (1988). The water and electrolyte
metabolism of captive and free-ranging white-browed scrubwrens Sericornis
frontalis (Acanthizidae) in arid, semi-arid and mesic environments. Aust J.
Zool. 36: 29-51.
Ambrose, S. J., Bradshaw, S. D., Withers, P. C. and Murphy, D. P. (1996).
Water and energy balance of captive and free-ranging Spinifexbirds
(Eremiornis carteri) North (Aves:Sylviidae) on Barrow Island, Western
Australia. Aust. J. Zool., 44: 107-117.
I realize that the Spinifexbird (2nd reference) is not an acanthizid, but I
just wanted to demonstrate to you that other small passerines have similar
strategies for maintaining body water balance.
One of the difficulties that small birds have in eating invertebrates is
that their diet is also high in sodium (salt). Excess salt in the diet has
to be excreted in the bird's droppings which, in turn, requires the
excretion of water. The few studies that have been carried out on
Australian birds show that insectivorous species that live in the arid and
semi-arid zones have more efficient kidney function than those that live in
the temperate zone (hence able to excrete excess sodium from their bodies in
higher concentrations) and can also tolerate higher concentrations of sodium
within their bodies without the need to excrete a lot of it. These
adaptations help these birds to conserve body water.