Let me explain a bit further.
From a "human" standpoint, if you were to have your DNA tested, both your mother and fathers DNA would be present.
So, from practical standpoint, scriptures tell us that Jesus was "conceived" of the Holy Spirit.
"And the angel answered and said unto her, The Holy Ghost shall come upon thee, and the power of the Highest shall overshadow thee: therefore also that holy thing which shall be born of thee shall be called the Son of God." -Lk. 1:35 (KJV)
In the Greek, the word "overshadow" means:
"Tropically, of the Holy Spirit exerting creative energy upon the womb of the virgin Mary and impregnating it, (a use of the word which seems to have been drawn from the familiar O. T. idea of a cloud as symbolizing the immediate presence and power of God): with the dat. Lk. i. 35."
Source
Thayer, Joseph Henry.
A Greek-English Lexicon of the New Testament, being Grimm's Wilke's Clavis Novi Testamenti, translated, revised, and enlarged. Corrected edition. New York: American Book Company, 1889. This complete, unabridged digital edition adds transliterations, Strong's numbers, and unicode Greek characters. These additions are ©2007 TheBible.org, all rights reserved worldwide.
Even one NT apocrypha books testify that Jesus was preforming miracles when He was but a child. (I only mention this as, not that I believe any apocrypha books)
Even John the Baptist was full of the Holy Spirit in the womb. (cf. Lk. 1:15)
And to go a bit further, scriptures say that immediately after being presented in the Temple as per the Law:
"And when they had performed all things according to the law of the Lord, they returned into Galilee, to their own city Nazareth.
And the child grew, and waxed strong in spirit, filled with wisdom: and the grace of God was upon him." -Lk. 2:39-40 (KJV)
And here, the context mandates that Jesus was already filled, and continued to "strengthen":
"to strengthen, make strong, (Vulg. conforto [and in Eph. iii. 16 conroboro]); Pass. to be made strong, to increase in strength, to grow strong: pass, with dat. of respect, πνεύματι, Lk. i. 80; ii. 40 [here G L T Tr WH om. πνεύ ματι]; δυνάμει, Eph. iii. 16,"
Ibid
And don't forget that Jesus was teaching in the Temple long before He was baptized. (cf. Lk. 2:46-49)
No, Jesus did not need an anointing of the Holy Spirit.
The trinity as seen at Jesus' baptism was a testimony from them (trinity) as to the acceptance of Jesus to be our Passover Lamb, and as a witness to His Messiahship.
God Bless
Till all are one.