That's because most of them are violent and a menace.... but there are some who arn't and our little fluffball is one of those who's merely a bit annoying. :-p
As to her being a pet previously, the princess already knows this, but she also knows that the person she was the pet to is the person who had the future prediction thingamjig.
So she knows If they did what you suggest, they'd never have any chance to find the predictive thing which the princess is looking for.
Also the mc has been kissing the princess butt since the start, so she trusts him to possibly find the thing by befriending the fluffbal.