Do you need evil for a fawn or deer to exist? Without evil many animals would live peaceful happy lives, not harming anything and living in balance with nature.
Some might say "without animals to hunt them, they would overpopulate and eventually starve", but even the animals that eat them are not evil, they are just hungry and kill only for food, not sport.
So yes, you can have good without evil, and no, the definition of good isn't based on something to compare it with. Good is simply the act of existing in harmony with the life/universe around you, without disrupting the lives of others and causing more suffering than is needed for life to continue.
Evil is being selfish, harming others because you want something and think your own happiness is more important. Evil is going against nature and making the universe a harsher place. Evil is usually a concious act by man or animal to cause harm to others (or even yourself).
Evil can not exist without good, that is true, as without anything good in the universe, there would be nothing to harm, there would be no basis for evil at all. Good on the other hand is the natural state, and evil is the abomination, the mutation, the other path. Evil is when you take something good, and twist it, to make it a negative instead of a positive.
Sadly evil is common and even the best people often commit at least some evil acts. Animals on the other hand are more simple and while there are certainly animals that commit evil acts (cats, rats, birds etc) some animals rarely do, or never do.
A world without evil might be dull, but it would certainly be safe and everything living in it would be happy. It would not have to be totally boring though, there could still be happiness, achievements etc, just most competition would be for fun at most, and progress would almost certainly take much longer (especially technological progress etc, since no wars etc).
We could probably create such a world, almost definitely with the tech we have now, but evil is so ingrained in us that it's not very likely to happen, especially since most of those in positions of power, get there by doing many evil acts and believe that makes it their right to control everything.