Yes you can. Once you lose one of the required rare cards to the Card Queen she will leave the area and go somewhere else. If her new location is Dollet then you can either win back the rare card you lost to her previously, or win the rare card you just unlocked from her (but not both, as she will leave again after one has occured).
If she goes anywhere other then Dollet your options are simpler. You can follow her to the new region and win the rare card you unlocked from her, or go to Dollet while she is not there and win back the card you lost to her, by playing her younger brother (the son of the grumpy painter, that lives down the strip just near the beach). I believe the general rule is that he will have all the rare cards you have lost to the Card Queen, so long as she is not actually in Dollet.
Its been a while since I played, but I believe thats how it works. I’m sure someone else will correct me if I’ve forgotten something.