You can stuff it with sphagnum moss and grow some form of vines on it. Are you familiar with the process of preparing a wire basket,in which you line the sides with sheet moss and fill the middle with potting mix. It's a similar process with these wire frames. Use a chop stick to poke holes afterwards to plant your vines. In warmer zones like where you are, a creeping fig will do just great. Or you can use baby's tears. Or some form of succulent like echeverias, or a combination of many types of succulent. Some like to use mondo grass to form 'hair'. With this type of topiary, you have to be careful of keeping the plant moist but not overwatered. They do tend to dry out very quickly.

Or maybe you can just let a vine grow up on it like it was on a trellis. Just shape the plant to keep the shape close to that of a giraffe.

Another form of topiary which can be considered a more permanent type of planting is to take 1 or 2 choices of shrubs that can be grown to follow the shape of your giraffe. This process though will take years to accomplish. You'd need to find an evergreen shrub (that reaches 6 ft or taller) in your area like a yew, maybe a holly. You'd have to do research to find a suitable plant. Choose one with multiple branches that can be manipulated to conform with the shape of the giraffe. Since there are 4 'legs' then you'd have to purchase 4 plants.

Hope this helps. Good luck.