That’s as good explanation as any for the rhetorical “who knows that” question of Solomon. Solomon didn’t produce any prophetic writings to our knowledge, but he was a skilled theologian and compiler of wisdom sayings (proverbs). I am not familiar with Hebrew lore of that time about the animals.
Here's the entirety of it from the King James, for the benefit of those who are unfamiliar:
1 To every thing there is a season, and a time to every purpose under the heaven:
2 A time to be born, and a time to die; a time to plant, and a time to pluck up that which is planted;
3 A time to kill, and a time to heal; a time to break down, and a time to build up;
4 A time to weep, and a time to laugh; a time to mourn, and a time to dance;
5 A time to cast away stones, and a time to gather stones together; a time to embrace, and a time to refrain from embracing;
6 A time to get, and a time to lose; a time to keep, and a time to cast away;
7 A time to rend, and a time to sew; a time to keep silence, and a time to speak;
8 A time to love, and a time to hate; a time of war, and a time of peace.
9 What profit hath he that worketh in that wherein he laboureth?
10 I have seen the travail, which God hath given to the sons of men to be exercised in it.
11 He hath made every thing beautiful in his time: also he hath set the world in their heart, so that no man can find out the work that God maketh from the beginning to the end.
12 I know that there is no good in them, but for a man to rejoice, and to do good in his life.
13 And also that every man should eat and drink, and enjoy the good of all his labour, it is the gift of God.
14 I know that, whatsoever God doeth, it shall be for ever: nothing can be put to it, nor any thing taken from it: and God doeth it, that men should fear before him.
15 That which hath been is now; and that which is to be hath already been; and God requireth that which is past.
16 And moreover I saw under the sun the place of judgment, that wickedness was there; and the place of righteousness, that iniquity was there.
17 I said in mine heart, God shall judge the righteous and the wicked: for there is a time there for every purpose and for every work.
18 I said in mine heart concerning the estate of the sons of men, that God might manifest them, and that they might see that they themselves are beasts.
19 For that which befalleth the sons of men befalleth beasts; even one thing befalleth them: as the one dieth, so dieth the other; yea, they have all one breath; so that a man hath no preeminence above a beast: for all is vanity.
20 All go unto one place; all are of the dust, and all turn to dust again.
21 Who knoweth the spirit of man that goeth upward, and the spirit of the beast that goeth downward to the earth?
22 Wherefore I perceive that there is nothing better, than that a man should rejoice in his own works; for that is his portion: for who shall bring him to see what shall be after him?