To waddle is to walk with a duck-like gait. The word also works as a noun denoting the duck-like walk. A wattle is (1) the fleshy, wrinkly fold of skin hanging from the chin of some birds and lizards, (2) a construction of poles intertwined with twigs, reeds, or branches, and (3) any of various Australian shrubs or trees of the genus Acacia. Waddle is more narrowly defined, always pertaining to the way of walking, and wattle is rarer.
If it helps in remembering them, note that the two d‘s in waddle resemble two feet.
Examples
By the time you waddle out of Pampa Brazilian Steakhouse, you may not want to look at a filet of beef or tenderloin of pork for several days. [Edmonton Journal]
Savoia said she escaped from her car after waiting a few minutes for the swans to waddle away. [Boston Globe]
But his audience is soon distracted when half a dozen pelicans skid in to land on the water, and waddle up to wait for breakfast. [New Zealand Herald]
The president then made his way over to the bird, giving its head a pat down as he quizzed its owner about the wattle. [Los Angeles Times]
We know, too, that they increasingly lived together in relatively substantial settlements of wooden houses, lined with wattle and daub and with thatched roofs. [Irish Times]
These days council give new citizens such gifts as boomerangs, gum and wattle tree seeds, and other reminders of Australiana. [News.com.au]