Kiddushin 19a - Kattan making a Kinyan

Tosafos proves from the fact that a ketana is able to accept her own kesef kiddushin, that when there is a da'as acheres being makneh something to a child they are able to make a kinyan m'doraysa. Tosafos proves this from the gemara in gittin 65a where r' chisdah holds a child can be koneh m'doraysa even without da'as acheres makneh, so when there is da'as acheres makneh all would agree that he can make a kinyan.

This issue is actually a machlokes rishonim. Based on the gemara in Succah 46b, the Shulchan Aruch 658:6 rules that one should not give a lulav to a child prior to being yotzei himself, because the child can be zocheh but cannot give back. However, if the child reached an age of "pe'utos", the Shulchan Aruch quotes a machlokes as to whether he can give back. The Rambam holds that he still cannot give back, whereas the Ran holds that he can. Why would the Rambam say that he cannot give back, since the gemara in gittin states explicitly that the Rabbonon instituted that a child who reached pe'utos can be makneh to others? The Biur Halacha explains that the Rambam holds that with da'as acheres makneh, the child is zocheh m'doraysa (like our tosafos) and therefore even if he reached the age of pe'utos, he can only return it m'drabonon. Since m'doraysa it would still belong to the child, the adult cannot be yotzei with this lulav. But the Ran holds even with da'as acheres makneh the child is only zocheh m'drabonon, therefore the ability to give back m'drabonon (when he reaches age of pe'utos) is sufficient. Based on this approach, it would seem that if the father already gave the lulav to the child who did not reach the age of pe'utos, the Ran would say that the father should still use the lulav since he owns it m'doraysa, and perhaps would even be able to make a bracha on it.

Another approach to understanding the opinion of the Ran is that he holds that although the child was koneh on a d'oraysa level, he can give it back m'drabonon and that would be sufficient because a kinyan d'rabonon would work m'doraysa. This could even be the point of argument between the Rambam and Ran.

It would also seem that according to the Rambam where the child who reached pe'utos can't give it back because he is zocheh m'doraysa and not just m'drabonon, that is only because of da'as acheres. So, if the father would be mafkir the lulav and allow the child to take it so that he is only zocheh m'drabonon, then even the Rambam would agree that the child can return it once he reaches the age of pe'utos (which would be a solution for a situation where the father for whatever reason couldn't fulfill his mitzvah before letting the child use it).

Based on the assumption that a child can only acquire m'dorabonon even with da'as acheres being makneh, the gemara would have to be explained that the girl can receive her kiddushin money m'din areiv (cosigner) as Tosfaos originally entertains.