Well, this should help solve the mystery:
The uniform the soldier is wearing is a Japanese Imperial Army uniform, dating from 1905-1939. After 1939, the kepi (the type of hat worn by the soldier), was changed to a much shorter style. Judging by the picture, the kepi looks to be from around the WWI era. This could be confirmed if there is a 5-point star on the hat, which I can't tell from the photo. However, the cannon appears to be pre-WWI.
This suggests that the item in question was a commemorative plaque made to commemorate the 1905 Treaty of Portsmouth, which was a treaty signed in the U.S. (in Portsmouth, NH) by the emporer of Japan and the czar of Russia. The treaty was brokered by President Theodore Roosevelt, which ended the Russo-Japanese War. Roosevelt was awarded the Nobel Peace Prize shortly thereafter. This treaty also strengthened US-Japanese relations, which would explain the presence of the Statue of Liberty.