Furniture from Eucalyptus wood?  

I think the thing I'd be keen to stress is that drying out lumber like that either requires kiln drying or years of drying it, as far as your 'considerable period' goes. And as I understand it drying isn't the issue exclusively: while lumber can be dry within a few years, how it shifts after it's dried is equally important.

Eicalyptus is known to be very unruly wood. They tried to grow eucalyptus for railroad ties and the resulting ties tended to throw the railroad track, and they split from the spikes:

http://legacy.sandiegouniontribune.com/uniontrib/20080831/news_lz1mc31we...

But don't let the challenges stop you. You need to be prepared to begin the drying process properly as soon as you cut down the tree, not the next day, or the next.