mynachos some rather odd and unfeeling responses here! Very surprised.
YANBU in feeling very upset about this and that the staff did not behave in the way they should, you said they only seemed sorry when you mentioned the accident book.
Of course it was an accident, no one at all thinks the waitress did it on purpose but clearly she was rather stupid to put hot gravy next to a toddler.
The fact your dp was not as bothered about it as you is no measure that you were too bothered, IMHO!
However, what could be achieved by complaining? They may compensate you for you or your son's meal. But the actual meal is now over anyway. If you do choose to complain I would feel it may be more effective to put it in writing, rather than a phone call.
If you choose to do this, I would suggest making it clear you realize it was an accident but you hope training will be put in place to ensure this type of accident doesn't happen again and staff know what to do.
At the very least the staff should know not to put ice on a burn, even though you asked for it, they should advise against it as it does not help a burn to heal. If the individual staff do not know what to do in a situation like this, then the management should.
I once burn myself on a teaspoon that had fallen into the flame of a candle, in a restaurant. It ruined my meal as I spent almost the whole time in the toilet with cold water running over my finger.
If your son calmed down after ten minutes then it sounds like he was not too badly hurt.
Choose what course of action will be best for you and do it, either let it go and move on or contact the restaurant.
Accidents do happen and people do make mistakes but when possible restaurants do try to avoid hurting customers. (I have worked in several restaurants).
If you feel the staff (in general) did not respond well then there is no harm in saying this while acknowledging it was an accident. I am sure the waitress feels bad, but that is not the point. Would be good to know they have learnt from this.
www.coolburns.com.au/first-aid-for-burns/burns-faq