There are lots of ways to stiffen a piece of beadwork. Since I have heard both pros and cons for each of them I will give you a list to read up on them and decide what is best for you.
Future® floor finish (wax) method
Restitch the piece until it is stiffened (This is not always an option on brick or peyote pieces.).
AIleene's Stiffener products.
Apply the work to a piece of fabric with plastic, wire, or pellon sandwiched inside.
Personally, I usually try to work a bit snugger on work I know needs to be firm, and use as large a weight of Fireline as I can to give the worked piece body and firmness. Often this is enough.
Here is the same design in a chart for a bracelet. It would make a nice piece to wear around the holidays. There is space underneath the angel to add the year.