The only difference after a gallblader-removal is that your body won't be able to take up as much fat per meal as before, since there is no longer a reservoir of bile used for dissolving the fat. If you eat a meal with more fat than your body is able to dissolve for uptake, it will simply pass through your intestines and end up in the stool.
However some may feel pain/discomfort when eating af meal rich in fat. Also it is still possible to produce gallstones even after the gallbladder has been removed. So in general it is probably a sound approach to keep your diet low in fat. The type of fat shouldn't matter in this respect, as they all need bile for digestion (except medium chain triglycerides).
If you try to keep a low fat diet, you should probably take some supplement of the fat-soluble vitamins (A, D, E, K). Also it might be a good idea to make sure you get enough omega 3 & 6 fatty acids (fx by using a little bit of walnut oil on a salad).
I'm sure your nutritionist will be able to tell you more, but as far as I know, the above covers the basic principles.
