I guess you could send now but it's preferential to wait and send on Christmas day. If you know you'll be too busy to do it tomorrow though then feel free to do it now.
In order of preference:
1. Send on Christmas day (bonus points for figuring out their GMT and making sure it's Christmas day wherever they are)
2. Send ASAP before Christmas day if needed so they have it for Christmas day.
3. Send anytime after Christmas up until the 29th of December which is the deadline of the event. Failing to send once this date is reached will be bad.

How it works:
Everyone on the list has received a name of someone different to send to.
One person on the list has received your name and will send stuff to you.