Leanne, we did this birthday gift idea last year at Cinderella's Royal Table for my niece's 3rd birthday. I bought her a Cinderella figurine playset and wrapped it in princess paper and asked the CM if Cinderella could give it to her. She said no, because it would upset other children who might see Cinderella giving her a gift but not giving one to them, so Disney policy was that characters can't give gifts. However, she said that SHE would come over when the characters arrived at our table and bring her the gift and tell her that it was from Cinderella. Whenever she plays with that toy, she announces that Cinderella gave it to her.
It's a great idea, and I know that everything always just depends on what cast member you get, but if yours tells you that Minnie isn't allowed to do that and doesn't suggest the other, there's an idea for you to ask her for backup -- ask her to bring it over while Minnie's there and say Minnie wanted him to have it.
Thanks everyone for your comments and voting thus far -- it's looking promising, so I think we'll keep this ressie and hope for the best, but NOT tell her in advance that Minnie will be there so she won't be disappointed if she's not.
This is the only character meal where Minnie wears her Minnie dress, and Mickey's there too, right? She has the red with white polka dots Minnie dress to wear there and wants to see Minnie while they MATCH, so Minnie in colonial dress or her swimsuit just won't do for that.

And she needs Mickey too.