Little Lambcat

"Mary had a little lamb,
little lamb, little lamb,
Mary had a little lamb,
whose fleece was white as snow.
And everywhere that Mary went,
Mary went, Mary went,
and everywhere that Mary went,
the lamb was sure to go."

I've been trying to understand the meaning of this song but I fail to do so. I am the only Mary in the World as you may know and I haven't got a lamb so I ain't got a clue where did they got their inspiration from.

Who sang this blasphemy anyway? Is this supposed to be funny?
And who is Sarah Josepha Hale? What kind of name is Sarah?

I do have a little cat and if they want to change the lyrics to "little cat" I'll be more than pleased to retract my allegations... At least until my cat dies, that song would make me unhappy if I hear it at that time.
Also they should change the part where it chases me because my cat is anti-social and she doesn't leave the house either, even if she did the only way she could follow me to college was if she jumped in the bus and then catch the subway, which I don't think it's possible.
So the realistic update of the song would have to be something like:

"Mary had a little cat,
little cat, little cat,
Mary had a little cat,
whose fur was white, brown, grey and yellow as (insert something like that here).
And everywhere that Mary went,
Mary went, Mary went,
and everywhere that Mary went,
the cat was sure to stay at home sleeping somewhere."

Beautiful! Please make the proper corrections now and I'll contact you later for copyrights.