I think that Sunny could do very well in agility, definitely!
However, if you're thinking about breeding her, her pedigree is very informative. The pedigree helps to give us a rough genetic picture of what's behind a dog - not just what your dog, today, is like, but what's been passed down to her, and what she might pass down to her puppies.
Yes, there is one titled dog in this pedigree. However, that's only
one dog - and he's in the third generation, far removed, relatively speaking, from your dog.
Yes, you can have great dogs that never compete and are never titled. However, titles (or lack thereof) tell us a lot about the dogs and what they might have been like: a dog with lots of titles (I'm thinking performance here) is a dog who was owned by someone who took the time and energy to train the dog and compete with him, to test him, to prove his mettle. A dog with lots of titles is a dog who had the intelligence, athleticism, obedience, and drive to get the job done. A pedigree that has multiple dogs with titles is a pedigree that is likely to have produced a dog who will be able to produce quality puppies.
But titles don't tell the whole story. When you look at a pedigree, you should be finding dogs - or at least kennel names - that are recognizable. You should be able to see the rhyme and reason of why breedings were done: this family joined to that family, this line bred back upon, that that trait bred away from. You should be able to call up a mental picture of what the "heavy hitters" in the pedigree looked like. This is part of why education about the breed is vital if you want to produce quality animals: every dog exists in a genetic context, as part of a larger lineage, and you need to be able to look at the pedigree and understand what's in it. The pedigree is not just a collection of names, it's a record of what went into the making of your dog.
Here's a great example of a fantastic performance pedigree (chosen at random from the website of a breeder known for performance and conformation Shelties). There are
lots of titles here, and not just conformation titles. Heck, the performance titles include agility, obedience, and herding - these are some accomplished dogs! There are also three ROM producers (dogs who have produced a certain number of conformation champions) and a specialty Best in Show winner. The dogs in this pedigree have (assuming health clearances)
earned the right to perpetuate their genes. What's more, the kennel names and the dogs that dominate this pedigree are highly recognizable and respected - I know who these dogs are, I've seen them in the flesh, and I know their breeders for having produced excellent dogs. If I were thinking of buying one of these puppies, I could picture in my mind what they would look like, what their potential faults and virtues might be, and what dogs I might breed them to in order to take the next step in the lineage.