I haven't listened to it for a while, but singing it through from memory I think it's just a syncopation that moves the second "through" forward a beat and elongates it. There's no dropped bars or beats.

Here's what I think is happening (roughly) with the beats, with some subtleties missed out (for example, I've not tried to get the right rhythm on walking, just indicated the counts).

  3   4  1  2  3      4 1   2   3    4   12 34 +
  And together we'll go walking thro-ugh DixieLand
  
  1   2  3 4   12 34 + 
      Thro-ugh Dixieland