The date and year are slightly off. :)
Jamuna bridge in Delhi was opened on 1/1/1867 and passenger services commenced about a month later, so Kalka mail -proper did not start before that.
And through trains (without any breaks in between for river crossings ) between Howrah and Shahdara were operational from August, 1865 itself. The date of inauguration on IRI doesn't really have any significance. :)