There are two early instances in Act I in which Shakespeare establishes the strong bond between Celia and Rosalind, a bond that underpins the whole play, although Celia does slip to the background once they get to Arden.
In scene ii, Rosalind is downhearted because her father, the rightful Duke, is in exile in the forest of Arden. Celia admonishes her to be "merry." Rosalind responds that until she can forget her father, she cannot remember joy: "Unless you could teach me to forget a banished father, ...."
Celia elaborates upon their friendship to show the strong bond between them. Celia reprimands Rosalind and says that if their roles had been reversed, as long as Rosalind was still with her, she would have found a way to be happy for the joy of Celia's company and would be happy for Celia's sake. As proof of her love for Rosalind and as an inducement to cheerfulness, Celia tells Rosalind that Celia's inheritance will all be handed over to Rosalind as rightful owner of the Duke's estate.
... when [Frederick] dies, thou shalt
be his heir, for what he hath taken away from thy
father perforce, I will render thee again
The second instance is in scene iii. Duke Frederick is still angry because Orlando overthrew and injured his champion wrestler and angry that Rosalind failed to dissuade Orlando from wrestling:
... I would fain dissuade him, but he
will not be entreated. Speak to him, ladies; see if
you can move him [to dissuade him].
As a result of these combined insults and the popularity Rosalind has with the populace, Frederick exiles her, as he did her father. [As an aside, Shakespeare leaves room for speculation about Frederick's true motive: Was he so angry about Orlando and Charles that he would see Rosalind's slight role as treachery and exile her for it? Or is he really worried about Celia's image before the people?]
Here Celia renounces her father and swears to flee with Rosalind. After the disclosures in scene ii, we are ready to believe that Celia would certainly do this for Rosalind because of their strong bond, a bond forged in childhood.
... Then open not thy lips:
Firm and irrevocable is my doom
Which I have pass'd upon her; she is banish'd.
Pronounce that sentence then on me, my liege:
I cannot live out of her company. (I.iii)