According to Wikipedia:
In particle physics, the history of quantum field theory starts with its creation by Paul Dirac, when he attempted to quantize the electromagnetic field in the late 1920s. [My emphasis.]
And according to Wikipedia's entry on Dirac:
He was the first to develop quantum field theory, which underlies all theoretical work on sub-atomic or "elementary" particles today, work that is fundamental to our understanding of the forces of nature. [My emphasis.]
So, it seems definitely wrong to credit Feynman with the "invention" of QFT. If one would have to give credit for that to anyone in particular, the above suggests that that should be (and is) Dirac.
Feynman's and other contributions to quantum electrodynamics are summarised here.
It seems that there is possibly another contender (than Dirac) for the title of "father of QFT": Pascual Jordan. See arXiv:0709.3812 [physics.hist-ph], pp. 12-15, e.g.,
Since this was a conference honoring Dirac, other speakers can be forgiven
for declaring Dirac to be the founding father of quantum field theory.
[I]t is important to keep in mind that Jordan was virtually alone at first in
recognizing the need for the extension of quantum theory to fields.