Ellen...

Given the genealogical import of those most heavy immigration years, it's somewhat remarkable to me that a higher priority hasn't been given to getting that census indexed. I empathize with your plight and an indexing of the NY State 1865 Census can't come too soon.

In fact, I started to map the Gowanus/East River/Redhook/Brooklyn Heights section of the Brooklyn 1865 Census to aid my own research.

As to your specific question, 6 Carlton is just south of the Brooklyn Navy Yard and, as per the following links, appears to be located in the 11th Ward in 1860...

http://www.bklyn-genealogy-info.com/Ward/St.index.1860.78.ht...

...and in the 11th Ward in 1867 as well...

http://www.bklyn-genealogy-info.com/Ward/1867.Ward.Bounds.ht...

Even better (and new to me as well), this 1865 Map of Brooklyn appears to have the definitive answer for Carlton St...

http://www.geographicus.com/P/AntiqueMap/NewYorkCity-johnson...

Good luck in your Ward 11 search ;-)