You might also try putting "@cat" in the search box. You'll find many songs plus a few "cat song" threads.

Here are a few of those:
The Siamese Cat Song (from Lady & The Tramp)
Señor Don Gato
How Can I Keep From Purring (Betsy Wellings) - the lyrics are in the forum
Tiger Rag
Alley Cat
Stray Cat Strut


Then there are songs about horses, e.g.:
Stewball
Run For The Roses (Dan Fogelberg)
Blood On The Saddle (Short but -- OK, not that sweet, either, but funny)
I Ride An Old Paint
Tennessee Stud
Run, Molly, Run


and about frogs:
I'm In Love With A Big Blue Frog (Peter, Paul & Mary)
Frog Kissing (country song)
Frog Went A-Courtin' (mentioned earlier in the thread)
It's Not That Easy Being Green (Kermit's song)