Is that your belief?
There is no reference in scripture to a position of "Queen" in the new Heaven, or the new Earth. There is no indication in Scripture that God desires, wants, or will have a "Queen", or that this "Queen" will serve with Jesus, the King of Kings.
Psalm 45:9 doesn't refer to God, it refers to David's earthly King, who did have a Queen:
Thou lovest righteousness, and hatest wickedness: therefore God, thy God, hath anointed thee with the oil of gladness above thy fellows.Note that God is referenced in verse 7, and is the God of the "thy" being referenced ("thy God"). So Verse 9's "thy" is the "thy" for whom God is God, not God. Putting them together, "God is your God, and on your right hand the queen stood".8All thy garments smell of myrrh, and aloes, and cassia, out of the ivory palaces, whereby they have made thee glad.
9Kings' daughters were among thy honourable women: upon thy right hand did stand the queen in gold of Ophir.
1st Kings 2:18-19 are not about "intercession", they are about a son wanting to ask his father to get a wife for him, and doing so through the King's mother.
Worse, the result of that "intercession" was that the King refused, mocked his mother for allowing herself to be used, and swore to kill the son for petitioning him through his mother.
Hardly an "example" of some exalted Queen sitting on the right hand of God from whom we should ask for intercession:
18And Bathsheba said, Well; I will speak for thee unto the king.Scripture is not impossible to understand.19Bathsheba therefore went unto king Solomon, to speak unto him for Adonijah. And the king rose up to meet her, and bowed himself unto her, and sat down on his throne, and caused a seat to be set for the king's mother; and she sat on his right hand.
20Then she said, I desire one small petition of thee; I pray thee, say me not nay. And the king said unto her, Ask on, my mother: for I will not say thee nay.
21And she said, Let Abishag the Shunammite be given to Adonijah thy brother to wife.
22And king Solomon answered and said unto his mother, And why dost thou ask Abishag the Shunammite for Adonijah? ask for him the kingdom also; for he is mine elder brother; even for him, and for Abiathar the priest, and for Joab the son of Zeruiah.
23Then king Solomon sware by the LORD, saying, God do so to me, and more also, if Adonijah have not spoken this word against his own life.