Glazed Pottery Bottle or Puzzle Jug with Hunting Dog Logs Redware

This is some type of ceramic or clay pottery vessel - possibly redware. It weighs about 4 lbs. It measures 9 1/4 inches tall x 5 inches x 5 inches. The dog's tail is broken off. The bottom has part of a paper label attached, but it has no writing. The dog's eyes and nose are open/pierced. The little smaller animal has pierced / open nose, and an opening at the back rear. There are openings/holes at the top of two of the logs, at opposite corners. I think this may be some type of puzzle jug or drinking game, as there are several openings or funnels throughout the piece.

I do not know the age nor the maker. Any help or information would be greatly appreciated.