Concepts or ideas can't be copyrighted. However, how that concept or idea is rendered can be copyrighted.
Unless otherwise clearly stated, practically everything you see or hear created in the last 75 years is copyrighted. There's no requirement to state something is copyrighted for it to be copyrighted. Art is copyrighted the moment it is created.
So, the concept of an animal peeking its head out of water is not something which can be protected. If your client wants a tiger, bear, baby, cyborg, etc... looking above water... then you would be fine exploring that idea.
Where you run into possible infringement is when you look at that sample, and try to mimic the way water is conveyed, the coloring, the depth of the head.. essentially anything similar can be seen as derivative work and therefore a possible infringement.
If the client is dead set on duplicating someone else's design, one possible aspect to convey to a client would to ask why they want a logo that is similar to another logo? The purpose of a logo is to be a unique identifier and merely copying some other logo defeats that entirely.
If I were to have a client dead set on replicating the artwork of someone else, I'd decline the project.
Non-profit, or not-for-pofit, organizations are bound by the same laws as any other organization. There is no legal "free use" clause merely because an organization is classified as "non-profit" for tax purposes. Infringement is infringement -- the tax structure of an organization does not change that fact.