Eating in the Garden of Eden was meatless as is explained in the verses below.
Genesis 1:29-30 And God said, Behold, I have given you every herb bearing seed, which is upon the face of all the earth, and every tree, in the which is the fruit of a tree yielding seed; to you it shall be for meat. 30 And to every beast of the earth, and to every fowl of the air, and to every thing that creepeth upon the earth, wherein there is life, I have given every green herb for meat: and it was so.
In Eden, food came from plants. This was true for the land animals too. Some may scoff that some animals cannot survive without meat. That may be true in our fallen world, but not in Eden. Even in a fallen state, some animals which normally eat meat sometimes choose not to. (See No Taste for Meat and Unexpectedly Vegetarian Animals – What Does It Mean?) The prohibition against eating meat ended after the Flood of Noah. (Genesis 9:3) So there is no biblical reason to practice vegetarianism in our current dispensation.