<PERSON> answer is pretty much unassailable (can't top first-hand experience!) but here's a hand-wavery kind of answer that may give you some ideas for how to adapt your original idea:
1) Containment: as <PERSON> explained, you need a magnetic trap to contain antimatter, and it would be very difficult (if not outright impossible) for a living creature to sustain such power levels. So I suggest that the beast be engineered with plutonium slugs in its heavily-armored spine which can fuel the containment fields within its gut.
2) PewPew!: The beast could have a metallic weave internal along the antimatter-storage pouch, leading along its throat and out its mouth. When it wants to destroy something in front of it, it would stretch the normally spherical field into a needle-width tube that sprays an extremely narrow stream of antimatter (on the order of milligrams, as <PERSON> suggested). 300
The magnetic containment field would end shortly after its teeth, causing the antimatter to violently detonate in whichever direction the dragon was aiming.
3) Additional considerations: since the field would be passively supported by a nuclear reaction, rather than the dragon's organic processes, it would be maintained even in the event of the beast's death (as long as its gut or spine weren't blown up). In addition, it wouldn't have any way of generating its own antimatter, so it would have to be supplied externally (possibly it would be "born" with a 10g supply, and use only a few milligrams for a sustained burst).
4) An all-natural alternative: if you wanted to mix a fantasy and sci-fi setting, and have an antimatter-blasting dragon without needing genetic engineering, you could use the same suggestions above, with the additional caveat that the creature would slowly accumulate the necessary raw materials within its skeleton over the course of millenia. So, younger dragons would spew radiation clouds, older ones would be able to shape the radiation with magnetic fields, and ancient dragons would have a small amount of antimatter (accumulated over millenia) to fire.
Again, it's all handwavium, but hopefully there's something here you can use to bolster your original idea. 160