If we only take the grammatical structure alone into consideration, I believe the sentence is correct. For instance, We can say, " Give her the pen". Since “pen” is a noun we can replace it with a pronoun, hence, “Give her it”. But I have doubts about it because it sounds odd to me. I think it should be put this way: Give it to her.
I just wan’t to know if this (give her it) sounds natural to native speakers.
‘Give her it’ is said this way to indicate that the speaker is being abrupt and sounding irritated.
The usual construction as an imperative is: Give it to her but if you have lost your temper and want the ‘giving’ to be done immediately because you can’t be bothered to wait any longer, you would say: Give her it!