I looked the music for this song up. I think Kipling chose it working back from an incident in the final story in Stalky and Co, for which he wanted a tune that Stalky's messenger could play half of on a bugle and get Dickson Quartus to play the rest. There aren't that many tunes you could play most or all of on a bugle because of its restricted range of notes (no valves, so natural harmonics only), but "Mind the Baby" is indeed one of them.