Final answer:
Before administering intravenous potassium, the highest-priority item a nurse should check is the child's serum potassium level to prevent hyperkalemia and ensure safety.
Step-by-step explanation:
The highest-priority item a nurse should check before administering intravenous potassium to a child with hypertonic dehydration is c) Serum potassium level. This is because serum potassium levels are critical and closely regulated by homeostatic mechanisms. Potassium imbalance can have significant effects on cardiac and neuromuscular function, hence the importance of ensuring the serum potassium is not already high before adding additional potassium to the system. The nurse might also check urinary output to ensure the child's kidneys are functioning and capable of excreting the extra potassium, especially in children whose renal function can be compromised, like in the case of dehydration. However, serum potassium levels are a more direct measure of the immediate need for supplementation and potential risk of hyperkalemia.