There are great poems about dogs. I don't mean of the sentimental variety. I'm against sentimental poems about dogs on principle (it is too easy) but I can be willing to make an exception. However the domestic cat is a less common subject for literary inspiration. T.S. Eliot's Old Possums Book of Practical Cats is terrific fun. Sadly, I don't think that is will recover from being Andrew Lloyd Webber-ized, at least not during my lifetime.
Cats have lagged behind their canine domesticated companions lacking in solidity or depth or complexity or nuance or whatever property is needed to carry the burden of being poetic subjects. We have been drawn instead to its wild ancestors -- tigers and panthers. Cats have been more useful as figures -- metaphors, images -- than as objects in and of themselves and I suspect that this has something to do with the nature of cats.
There are two great poems about the domesticated cat: Marianne Moore's "Peter" and the unparalleled section of Christopher Smart's Jubilate Agno, "For I Will Consider My Cat Jeoffry." It is unfair to put them side by side because I don't want to diminish the pleasures of Moore's poem and there is really nothing that compares with Smart.
I would recommend reading them on separate occasions. Also Moore demands more of her reader, at least at first reading the Moore appears more difficult. Smart is more complex than it seems, but it depends on how you want to read it. It is, also, quite frankly, madness. Moore does not give you choice. I find that is part of the pleasure in reading Moore, that she is so exacting.
"Peter" by Marianne Moore
"For I Will Consider My Cat Jeoffry" by Christopher Smart