The British Library has in its collection sheet music for a song called A COTTAGE IN THE COUNTRY (THAT'S THE THING) by Walter Donaldson (New York: Donaldson-Douglas & Gamble, 1930).

There's also JUST A LITTLE COTTAGE IN THE COUNTRY CALLING 'COME BACK HOME', words by Andrew B. Sterling and music by Alfred Solman (New York: Joe Morris Music Co., 1917).

It seems unlikely either of these are the song you want. I would guess Isla Grant probably wrote the song she sings called A COTTAGE IN THE COUNTRY, but I can't confirm this.

You could write to Isla Grant through: her web site.