It's quite hard to assess how "bright" someone is when they were home educated, did not take usual exams (wartime) and did not go to university.
So instead you have to look at what they did in their working life. ER II was an excellent diplomat - stuck to the brief, met just about every world leader and never provoked international difficulties (compare Boris - a Kings Scholar reputed to be really brainy who just could not do this).
No indiscretions as head of state or in her governmental role. Clearly chose advisers well - look at the Aussie crisis of 1975
Must have excellent short-term memory - personal comments at investitures and receptions (another form of following the brief)
Can't think of any major bloopers with her charities and patronages - though amount of her time those really had is moot.
Then other roles - steering the Duchy and the management of other properties (see interviews with the key senior staff who explain that she took time to really learn/understand what went in to it, and took a real interest), being the owner/breeder of world-class racehorses
She said her main regret was following advice that her presence would impede, rather than following instinct and making an early visit to Aberfan (had since made several visit)
And in the aftermath of Diana's death, opinion remains divided on whether she showed good judgement (putting family ahead of nation for once and staying with the princes) or whether she was remote and uncaring.
Sorry - all a bit stream-of-consciousness - but I don't think you can write-off ER II as not very bright because she had no formal education or academic achievements.