Particularly when the engine is cold, it is run at higher idling to bring it uo to working temperature, where the engine is more efficient. So it is not good to let it race away in neutral. Get the car in gear and get moving!
As both of you said the problem goes away after the car starts rolling, does not behave so when the engine is warm, and is not violently vibrating when the problem is there, I don't think it is a cause for worry. Just a check for points Binoy mentioned above during your next regular servicing would suffice.
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