1) The Maharsha writes that the Gemara here only had to say the Gezeirah of Chereshes-Cheresh-Pikachas according to the opinion that Beis Din does not have to prevent a minor from eating Neveilos (Yevamos 114a). According to the opinion that Beis Din is commanded to prevent the Katan from eating Neveilos, we can say that the reason why a Cheresh is not fed Terumah d'Rabanan is in fact because of a Gezeirah to prevent him from eating something prohibited mid'Oraisa.

2) The Maharam (in Tosfos DH Dilma) writes that we see indeed that our Sugya holds "Katan Ochel Neveilos Ein Beis Din Metzuvin l'Hafrisho" from the fact that the Gemara here (seventh line) asks, "Let her eat! She is a 'Katan eating Neveilos'!" which shows that the Gemara here follows the opinion that the Beis Din does not have to stop the Katan.

3) Here is an answer according to the Rambam and Aruch la'Ner:

a) The Rambam (Hilchos Terumos 6:4) phrases the Halachic conclusion of our Gemara in a suprising way. He writes:

"A Chereshes or Shotah who married a Kohen may not eat Terumah even if her father married her off to the Kohen. This is because of a Gezeirah that a Kohen Cheresh might marry a Chereshes and feed her Terumah."

b) The Kesef Mishnah asks on the Rambam that this is not the conclusion of our Gemara, since the Gemara asks immediately on this Gezeirah about the Cheresh and Chereshes, "Let her eat?! She is a 'Katan eating Neveilos'!" (which we do not have to prevent from happening).

c) The Aruch la'Ner here answers with the help of the Tosfos Yeshanim (Yoma 82a, DH Ben) who writes that even according to the opinion that the Beis Din is not obligated to stop the minor from eating Neveilos (in fact, the Rambam rules like this opinion in Hiclhos Ma'achalos Asuros 17:27), this Din applies to Beis Din, while the father is obligated to educate his child. Part of this Chinuch is to prevent him eating forbidden foods.

d) However, according to this, it is difficult to understand how the Gemara here can ask, "Let her eat! She is a 'Katan eating Neveilos'!" because this is sufficient reason why the Beis Din does not have to stop her but the father should still have the Mitzvah of Chinuch to prevent his daughter from eating Terumah. The Aruch la'Ner answers that there is a difference between the Gemara and the Rambam. The Gemara (beginning of 113a) discusses a Ketanah and a Chereshes together. Rashi (DH u'Mai Shena) writes that the mother married off her minor daughter. It must be that the girl has no father. So there is no father either who has a responsibility to ensure that the Chereshes does not eat forbidden Terumah. In contrast, the Rambam discusses a girl who has a father, as he writes that the father married the Chereshes to a Kohen. Therefore, the father must ensure that his Chereshes daughter does not marry a Cheresh who will feed her Terumah. This is why the Rambam cited an intermediate stage of the Gemara as his conclusion, because the Gemara refers to a girl without a father, while the Rambam discusses a Chereshes with a father.

e) According to this, we can answer our original question, becasue it is not enough merely to skip to the Gezeirah because of a d'Oraisa, since there is a more simple Gezeirah, that the Cheresh might feed the Chereshes when the Chereshes has a father.

f) The Aruch la'Ner concludes that there is a very practically relevant Halachah that we learn from here. A father is obligated for Chinuch with his Cheresh daughter, since she may recover and become normal.

Kol Tuv,

Dovid Bloom