From Germany, but from what i know is that its alot easier applying in Straya especially as an american and since there isnt any deadline i know of, so you should be eligible, you can sign up on the actual australian immigration website if im not mistaken but id suggest looking it up yourself. However when it comes to NZ im not sure myself since the people i know that moved there from South America moved there under several government programs, but i would guess that its probably similar.
Heres the link for the Australian Immigration application:
https://immi.homeaffairs.gov.au/visas/getting-a-visa/visa-listing/work-holiday-417
And here the New Zealand one:
https://www.immigration.govt.nz/new...united-states-of-america-working-holiday-visa
Dont count on my Words since im from neither Country but its probably alot easier as an able bodied american to get a visa for both.
See if youre eligible and if its for both look which Country youd find most interesting.
Also before i forget to mention, pretty much any Country in Europe is fairly easy to get into as an american if youre willing to go to non english speaking Countries.