Not off Dog Of Two Head but a single from at least 21 months earlier.

I found this info online:

7 inch vinyl single - PYE 7N 17907
Released: 6 March 1970
STATUS QUO
A side DOWN THE DUSTPIPE (C Groszmann) (2.03)
B side FACE WITHOUT A SOUL (Rossi/Parfitt) (3.07)
Producer: John Schroeder


"Down The Dustpipe was written by a song writer from New Zealand called Carl Groszmann, who was signed to Ronnie Scott's publishing company Valley Music. This track was the first release to underline the change of musical direction that Quo had undertaken with their live performances during the past few months.
With Bob Young once again featured on harmonica 'Down The Dustpipe' returned Quo to the charts in May 1970, when the single spent seventeen weeks in the charts. The track 'Face Without A Soul' had previously been released on the album 'Spare Parts'."

I used to see Status Quo live quite a lot in 1971 - 72 'cos my girlfriend at the time worked for their nanagement. I even attended a private filming at The Marquee for German TV. My favourite album was Ma Kelly's Greasy Spoon. This was when they performed a more diverse set, before they hit on the continuous 12 bar monotony that was to bring them riches!