Gonna Buy Me a Dog, by the Monkees.
I'll Be Dogone by Marvin Gaye.
That was the first one I thought of too.
https://www.youtube.com/watch?v=aTbBvPoxUkk
The Monkees ~ Gonna Buy Me A Dog
https://www.youtube.com/watch?v=5dPEDVg5N2k
https://www.youtube.com/watch?v=nSJC-YDcS80