Originally Posted by taxicabnumber

Do you mean the Platinum or Reserve card? The SkyMiles Gold card doesn't, as far as I know, come with a companion ticket.

Assuming it's the companion certificate associated with one of those two cards, then yes, the companion certificate is fully transferable* -- you just have to pay with an Amex card (any Amex card).

*This doesn't mean you can move the certificate to her account, but you can log in and book the companion ticket with your daughter and any other person as the two travelers.