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Just by combining the QS1 with the QS, there wouldn't be any change in your AAoA since the closed card would still appear on your reports for another 10 years. However, it would impact your Age of Oldest Account if the QS1 is your oldest tradeline. Since you are rebuilding, I am assuming you have other tradelines (open or closed) on your profile that are older than this 9 months old QS1; so no impact to Age of Oldest Account either. Potential benefit of combining these two cards would be that your QS individual utilization will improve and can positively impact your score depending on how much you intend to charge (and pay) on this card on a regular basis.
The three months difference is age isn't going to matter if you combine the cards. Closed accounts count toward account age stats as much as open ones do. By the time the older card is likely to drop from your report, the age difference will be meaningless.
If the combination were to result in you having less than three open cards, some might advise waiting until you had a replacement for the closed card. But that's not the case here. The overriding factor is the annual fee. Go ahead and combine.