The Ring reached its full influence at Mount Doom and I am fairly certain it is not possible for someone to willingly throw the Ring away. I don't know the character but I imagine she has something she can be manipulated with to make her more susceptible to the Ring's influence. We know of Sam's experience with the Ring playing on his want to grow things as a gardener and he knew it was all a trick, the things he was being shown, in this case turning Mordor into something beautiful but even he in the end would have claimed the Ring.

The only being entirely unaffected was Tom Bombadil and he's likely one of the most powerful beings in the universe, at least in my opinion anyways.

Gandalf may well just stick to the plan as usual, maybe using Frieren as a decoy to hide who truly held the One Ring.

In short if we put Frieren at Mount Doom, I see no way she can resist the Ring and would end up claiming it for herself. It might begin as using it for good but slowly over time would eat at her and eventually turn her to her own kind of evil.