There is a much more logical and simpler way to solve this using information already presented in the problem and with fewer assumptions. The mistake you made was with calculating the molality.
The best way I found to solve these problems is to use the factor-label or dimensional-analysis methods. If you have your units correctly, it should work every time.
You're given a 1.5M KI solution, so we can say you have 1.5 mol KI per 1000 ml of solution. Then, knowing the density of the solution, you can calculate the mass of the solution. At that point, you can calculate the number of moles of KI per 1000 g, or 1 kg, of solution and there it is you have the molality.
The calculation is setup as:
1.5 moles of KI 1 ml solution 1000 g solution
---------------- X --------------- X -----------------
1000 ml solution 1.18 g solution 1 kg solution
Then we cancel units:
1.5 moles of KI 1
ml solution 1000
g solution---------------- X --------------- X -----------------
1000
ml solution 1.18
g solution 1 kg solution
Then we plug and chug to get 1.27 moles of KI per 1 kg solution, or 1.27 molal.
The trick is setting up the expression so that the units cancel. Using this method, all you have to do is let the unit cancellation guide you until you end up with the units you want.
I was actually struggling with this a few weeks back, and to get better I worked through these practice problems I found on the web:
http://www.chemteam.info/Solutions/Molality-from-density-and-percent.htmlThey didn't use the factor-label approach explicitly, but it turns out the same.
Using this method, you don't have to worry about a change in volume, because the density takes care of it for you. I believe the rest of you approach is correct.