This is not correct, there are many stories where God perform deeds with/for animals too. For example,
Lord Vishnu is accompanied by the Shesha most of the time. If God is Rama then, Shesha is Lakhamana. If God is Krishna then, Shesha is Balrama and so on.
Most of the Gods' Vahana are Animals.
Lord Rama took help of Vanaras (monkey like) in Ramayana.
The Elephant Gajendra’s Crisis as described in Śrīmad-Bhāgavatam (Bhāgavata Purāṇa) 8.2:
SB 8.2.26 — Like a human being who lacks spiritual knowledge and is
too attached to the members of his family, the elephant, being
illusioned by the external energy of Kṛṣṇa, had his wives and children
bathe and drink the water. Indeed, he raised water from the lake with
his trunk and sprayed it over them. He did not mind the hard labor
involved in this endeavor.
SB 8.2.27 — By the arrangement of
providence, O King, a strong crocodile was angry at the elephant and
attacked the elephant’s leg in the water. The elephant was certainly
strong, and he tried his best to get free from this danger sent by
SB 8.2.28 — Thereafter, seeing Gajendra in that grave
condition, his wives felt very, very sorry and began to cry. The other
elephants wanted to help Gajendra, but because of the crocodile’s
great strength, they could not rescue him by grasping him from behind.
SB 8.2.29 — O King, the elephant and the crocodile fought in this way,
pulling one another in and out of the water, for one thousand years.
Upon seeing the fight, the demigods were very surprised.
SB 8.2.30 —
Thereafter, because of being pulled into the water and fighting for
many long years, the elephant became diminished in his mental,
physical and sensual strength. The crocodile, on the contrary, being
an animal of the water, increased in enthusiasm, physical strength and
SB 8.2.31 — When the King of the elephants saw that he
was under the clutches of the crocodile by the will of providence and,
being embodied and circumstantially helpless, could not save himself
from danger, he was extremely afraid of being killed. He consequently
thought for a long time and finally reached the following decision.
SB 8.2.32 — The other elephants, who are my friends and relatives,
could not rescue me from this danger. What then to speak of my wives?
They cannot do anything. It is by the will of providence that I have
been attacked by this crocodile, and therefore I shall seek shelter of
the Supreme Personality of Godhead, who is always the shelter of
everyone, even of great personalities.
Then Ganjendra offered prayers to God and as per following chapters,
SB 8.3.31 — After understanding the awkward condition of Gajendra, who
had offered his prayers, the Supreme Personality of Godhead, Hari, who
lives everywhere, appeared with the demigods, who were offering
prayers to Him. Carrying His disc and other weapons, He appeared there
on the back of His carrier, Garuḍa, with great speed, according to His
desire. Thus He appeared before Gajendra.
SB 8.3.32 — Gajendra had been forcefully captured by the crocodile in
the water and was feeling acute pain, but when he saw that Nārāyaṇa,
wielding His disc, was coming in the sky on the back of Garuḍa, he
immediately took a lotus flower in his trunk, and with great
difficulty due to his painful condition, he uttered the following
words: “O my Lord, Nārāyaṇa, master of the universe, O Supreme
Personality of Godhead, I offer my respectful obeisances unto You.”
SB 8.3.33 — Thereafter, seeing Gajendra in such an aggrieved position,
the unborn Supreme Personality of Godhead, Hari, immediately got down
from the back of Garuḍa by His causeless mercy and pulled the King of
the elephants, along with the crocodile, out of the water. Then, in
the presence of all the demigods, who were looking on, the Lord
severed the crocodile’s mouth from its body with His disc. In this way
He saved Gajendra, the King of the elephants.