I found an animal photo I'd like to use as an avatar. I only want to use the head of the animal and would retouch it a bit.
Is this considered as fair use?
Legally, it may or may not — you'd probably have to have a court case to determine your particulars. (The law simply isn't clear-cut.) Strictly speaking, you'd probably make de minimis arguments (I just used a small part; it wasn't really important; there was no commercial impact; it's only used in a small way) rather than fair use. But the court cases for that are (perhaps somewhat surprisingly) very strong on the side of the copyright holder.
Practically speaking, the odds of a court case happening are very small.
But why not find an image of the same animal type in the wide body of public domain and Creative Commons photographs? Then, you're definitely on the good side.
Personal opinion. IANAL.
I cannot see any reason why this would be "fair use".
You want to use somebody else's work.
If the work has a published licence that allows derivatives you may be allowed to use it. But that's not fair use. A published licence may stipulate share alike, or not, and attribution, or not. And more. But that is still not fair use.
From this US Copyright Office site that Omne mentioned you can get the advice below. I quote it here under fair use and it may be allowed under other terms as well.
Section 107 contains a list of the various purposes for which the reproduction of a particular work may be considered fair, such as
Without further information, constructing an Avatar does not seem to come close to any of these.
The most famous example of "Fair use" and image manipulation might be Barack Obama's "Hope" poster, designed by artist Shepard Fairey. When it was discovered that the poster had been based on a photograph by freelancer Mannie Garcia, and that the Associated Press held the copyright to that photo, the AP sought compensation and a multi-year legal battle began. In the end, Fairey pled guilty to charges related to this case and paid a fine, though I'm not sure the AP ever got any compensation.
In your case, you're probably unlikely to come under that sort of scrutiny if you're not earning money for your work and you're less famous than Barack Obama, but that's not going to really change the legal standing of your position. It's always best not to trust the legal advice of a bunch of random strangers on the Internet (go see a lawyer if you want real legal advice), but I think the practical advice given by others is pretty wise: just find a different image that's in the public domain.