I've used Soy Milk before, but never tried Non-dairy creamers - any help?
What about other type of pudding?
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I think it will work; you aren't really using any "fancy" properties of milk when you make rice pudding, it is mainly just serving as a liquid medium for the starch from the rice to thicken. Not saying it will taste great or be great for you, I think the soy milk, rice milk or almond milk would be more pleasant non-dairy choices, but I think it will work.
Non-dairy creamers are truly disgusting products. Read the ingredients. They're a horrid combination of sodium caseinate (chemically processed milk protein), artificial flavors, trans-fats, mono and diglycerides (gelatin), phosphoric acid, sodium alumionosilicate (anti-caking agent), corn syrup and stabilizers.
You might have found a better brand, or a vegetarian/vegan brand, but if you're using any of the standard grocery store brands, please don't. Try some almond milk instead.