Australia's Culture and Recreation Portal explains Easter, and in particular the unique Australian avatar of the season, the Easter Bilby:
For obvious reasons the rabbit was also a symbol of fertility and fecundity and became associated with festivals dedicated to celebrating the arrival of Spring. In Australia the rabbit is a pest, and celebrating it in any form denies the reality of Australia's rabbit plague and the damage rabbits do to Australia's fragile environment. The CSIRO estimates rabbit damage costs the Australian economy $AU600 million each year.
Because of this, a strong movement to replace the 'Easter Bunny' with one of Australia's own - the bilby - has developed. The bilby is a cute-looking creature with big eyes, big ears and a long tail and is a member of the bandicoot family.
The push for an Easter bilby was begun in 1991 by the Anti-Rabbit Research Foundation of Australia when they registered 'Easter bilby' as a business name and began licensing the use of that name for bilby-related products. The sale of the products was to fund research into wildlife conservation - an issue of importance to the bilby as bilbies are endangered, largely because of competition from rabbits and loss of habitat.
So instead of an Easter bunny delivering Easter eggs, they are now often delivered by a bilby, and Australian shops stock chocolate bilbies alongside chocolate eggs and rabbits.
As my own local population of wild rabbits has been wreaking particular havoc with my front lawn for the past year or more, I join in solidarity with our Australian brethren and their bunny boycott. Cute as those bilbies are, I elect to continue the Easter tradition that I established last year -- although it really isn't a "tradition" if you've only done it once, is it? -- by selecting a slightly different fuzzy critter for holiday display.
I have been unable to locate any 16th Century German illustrations of a bilby.