The sentence is correct.
When we report a yes/no question, we use 'if' or 'whether' followed by the subject and then the verb in the past tense (or present tense if the statement is still true). The original question uses the present simple tense ('Does... belong?'). In reported speech, this changes to the past simple tense ('belongs to'). The structure 'She asks her pupils if power in Britain belongs to the Queen' correctly follows this rule.