What you are looking for is spherification. You need to use a different hydrocoloid than gelatin. There are a couple of techniques you can use.
If you want solid spheres, you can mix your liquid with agar agar, which is readily available in the asain section of the grocery store, bring it to a simmer, and then use an eye dropper to drop the liquid in to a very cold olive oil bath (put it in the freezer). The dropping action will give you spheres.
You can also use a mixture of sodium alginate and calcium chloride, but those are harder to find and will need to be ordered online. The advantage is that you can make a sphere with a liquid center that "pops" just like real caviar. You mix the alginate in to your liquid and then mix the calcium in to a bath. You use the same eye dropper technique to get spheres. When the alginate and calcium touch, they instantly form a gel. This holds the sphere together. Leaving it for a couple seconds makes it thick enough to hold up.
All the info you need is available in this free recipe guide from Khymos.
I've actually done exactly this dessert before. You can see some of my lessons and issues in another question here. I did it a second time and opted to use a gelled peach (using agar agar) in the center for more of a maki presentation. Enjoy.