The Owl
The Owl is one of two title characters in this poem. The very first lines indicate that the bird has sailed to sea with the cat. It is also made clear that among the supplies they take with them are honey and a wad of paper currency.
The Owl has also brought along a small guitar. The Owl brings this out and begins playing it. It is through the song he sings that it becomes evident to the reader of the depth of his romantic feelings toward the feline companion.
The Owl openly admits his feelings by addressing the cat by the pet name, "my love." The Owl then goes on to sing about how beautiful the pussycat is by shortening her name to, simply, Pussy. Using this more familiar address, he reiterates over and over the extent to which he considers her to be beautiful.
The Pussy-Cat
Neither the Owl nor the Pussy-Cat is directly implicated by gender. However, the Owl's song extolling the cat's beauty seems to signify that the Cat is female. That, however, does not necessarily confirm that the Owl is male.
The Pussy-Cat extols the virtue of the Owl after the song using the term "elegant fowl" and addressing the sweetness with which the song has been sung. Immediately afterward, the Pussy-Cat exclaims the wish to be married. It is also indicated that the voyage in their boat will last for 366 days.
Pussy-Cat also brings up the subject of the marriage not being official unless they have a ring, which they do not. Upon landing in the strange land to which a species called the Bong-Tree is native, the two meet with a Pig that seems to possess the solution to this problem.
The Pig and the Turkey
The Pig does not appear until the end of the second stanza and, even then, he is only described as having a ring through his nose. When the Pig is asked if he would be willing to sell his ring for a shilling, he readily agrees.
The Owl and the Pussy-Cat take the newly purchased ring and make their way up a hill. At the top of the hill lives the Turkey. It is the Turkey who presides over the wedding ceremony which unites the Owl and the Pussy-Cat in holy matrimony.
The story ends with the now-married odd couple feasting hand-in-hand. As the day gives way to night, they have returned to the beach on which they landed where dance beneath the light of the moon.