No. If she asks, you can provide information resources or perspective, but don't push and don't tie it to your own decision. If for whatever reason, they don't like their decision, do you want it being blamed on you?
In these situations, I think we as parents have to make the best reasonable call for our own children. In your shoes, I would be separating this friend going or not from what's best overall for your daughter. Could a trial run be an option? It would seem like your DD may realize she's ready for third grade but is using "I'll only go if friend goes" to calm some nerves about it.
