I really like the look of these guys, and I haven't come across one yet.

Throdama come from the Portal on the Battlefield--to get a "wild" one you have to control the Portal for 10 hours.

You can also get them in Pet Trades (just search for throdama) or from the Pound. There aren't a whole lot of them in the Pound, so you have to either refresh the page a lot or get sneaky--you can search breeding offers, find a male you like, and check if he has any offspring in the Pound. (I think new players also have access to a full-site pet search feature, so you can do the same with that.)