I carry my laptop same distance as yours a couple times per week. Been doing it for years and never a problem. Arkel panniers, no special bag or padding although I do wrap it in a trash bag on rainy days. The only consideration I take for it sometimes in the winter is to give it 15 minutes to normalize temps before powering up, but usually the shower/cleanup time takes care of that. Not sure my laptop would like to spin up at 0F.
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Longbikes Slipstream