So, what do I have here? I'm not terribly well versed on these small queens yet. I know it's a 37, but beyond that, I need help. It measures a 12.5 perf on all sides, but I'm not going to kid myself that I have the valuable variety shown in my Unitrade catalog with that perf. It appears to be the wrong color for that anyway.
Your image makes it difficult to assess. Since you mention that your 3 c SQ is 12.5 X 12.5, I would appreciate knowing what gauge you used to measure your stamp and what about "shade" as the 3c has a lot !! Consulting Hillson and Nixon's "Canada's Postage Stamps of the Small Queen Era, 1870-1897", on page 128 there is a full chapter on Perforation 12.5 X 12.5, mentioning that in the first shipment of the Thee Cents, a small number were perforated 12.5 X 12.5.......with probably no more than 150-200 copies of this variety remaining.
Methodology in evaluating a 3 cent SQ is of importance as there exists so many perfs and shades !!
Hope more experienced members get into this discussion as I am not an "expert" of SQs but I do have some good references to help me, including the above book, also the "Canada"s Small Queen Era", 1870-1897, by George Arfken, and the "Color Guide for Canada Small Queens", by Richard Morris. These complement Unitrade Canada Specialized Cat.