Old song from childhood-

Old Captain Bob had a dog and a cat
With a big bow wow and a little meow.
They all lived together with never a spat
How in the world did they ever do that
With a big bow wow and a little meow
Meow, bow wow, meow bow wow etc.

Does that help?

"Big bow wow has been an expresson for some time, but can't find it in the 19th C. so far. An expression for a big winner, or top dog.

Perhaps Steve Gardham will tell us about Aird's "Big Bow Wow"-

BIG BOW WOW, THE. AKA and see "The Beardless Boy,""The Dissipated Youth [1]," "Giolla na Scriob," "Kate Kearney," "Priest avourneen," "Seanbhean Chrion an Drantain," "Stagger the Buck," ...... finds the first part of Aird's "Big Bow Wow" (Selections of Scotch, English, Irish and Foreign Airs, vol. 1, 1782, (104) to be the same as that of "An Cailin Deas Donn/The Pretty Brown Girl."

http://www.ibiblio.org/fiddlers/BI_BILE.htm