Are you shipping her homemade ice cream or store bought? Because if this is bought from a store or a chain I wonder if it wouldn't be cheaper to arrange from a shop in her city to deliver the ice cream from her.
There are insulating materials on the market, but I don't know whether I would trust them to keep the ice cream cold enough for long enough. It would be disappointing if she got melted ice cream soup.
The way I would go about it is to send it through courier, fedex etc. I think for international (small package) we pay them about $35-can't remember now.
When we send samples that have to stay frozen we use couriers and send the samples on dry ice (frozen carbon dioxide) in stryrofoam insulated boxes.
To be honest I can't imagine how this would be worth your while, send her roses and wait with the ice cream until you're together ;)