These are from FAQ's on the actual site for the program...
Program Terms & Conditions
Receive free admission* to one of the theme parks of Walt Disney World® Resort or the
Disneyland® Resort when you sign up and complete a day of volunteer service with a participating organization.
You must sign up for eligible volunteer opportunities for the “Give a Day. Get a Disney Day.” program through this site. Participation in volunteer activities outside of this sign-up process does not qualify for a free ticket.
Ticket quantities for this program are limited.
One ticket per person, regardless of the number or hours of volunteer service completed.
The program begins January 1, 2010 and continues until tickets are distributed or December 15, 2010, whichever occurs first.
Eligible volunteer opportunities are located in the United States, including Puerto Rico, or Canada only and you must have a residence in the United States, Puerto Rico or Canada to sign up.
You must be at least 18 years of age to sign up, and you may sign up a maximum of 8 additional members of your same household.
Children must be at least 6 years of age to volunteer under this program and receive a theme park ticket. Children ages 6-17 must be accompanied by a parent or guardian when volunteering. Other age restrictions may apply to certain eligible volunteer opportunities.
So it looks as though 5 1/2 is too young to participate. Maybe you could sign up for a date when your child is 6.
If you are looking to just find a place that will allow your child to help without a voucher, sign up for what interests you and just ask them if your child can come with. Most places will NOT allow younger children because of the liability. Hope this helps.