Thanks to some hard work by the DIscourse crew, your accounts avatars are no longer tied to Gravatar. To upload a custom avatar, pop into your account preferences and find your current one:
Hit the “Change” button next to it and upload your own:
I don’t believe animated gifs are supported, since the forum software resizes the images just like Vanilla, but IMO this is a good thing 
Thanks.
My avatar is now animated so I believe GIF must be supported. If you look closely the blue background should change to grey and back. It’s subtle so I don’t think it’s obtrusive but I can change it back to a still image if you prefer.
EDIT: It kind of looks shitty re-sized smaller or larger on my monitor at work so I may just change it when I get home tonight. 
Otherwise it looks good at the original 75X75…
Yep, looks animated to me!
I changed it back to a still image already. I couldn’t take the butchery the re-sizing did to the animated version anymore.
I may play around with it again when I get some time.
Where’s the option for the large, obnoxious and preferably animated signature?
Oh, that option is right here!
Size/dimension restrictions?
I don’t believe there are any, but the software automatically resizes the avatar. There are (IIRC) three separate avatar sizes used, one for display next to a post, and the other for display in infobars (the “in reply to” bar and others like that). And I think there’s a large avatar size used when you click on a user’s info page.
Just a reminder to everyone: update your avatars!
The stock Discourse avatars aren’t all that exciting. 