It definitely can be done if the toilet you have now is like what you have pictured. The waterline will need to be moved down to the side of the toilet (left side if facing the toilet, right side if sitting on the toilet). I usually put these about 6" from centerline of drain and 8" above finished floor. If you're going to be putting a one piece toilet in the waterline most likely will need to be further over than that. In addition, the waterline you have now for the toilet is 1". This will need to be reduced to 1/2" when you move it.
Now if this happens to be a wall mounted/carrier toilet, you've got a bigger animal to wrangle as the drain will need to be replumbed.