Right, that's exactly what happened. Same with corn and many other plant species that did not originally exist. They are all the result of selective breeding.
By the way, DNA isn't composed of proteins as (I think) you stated. Rather, it's a sequence of nucleotides, which are compounds consisting of a nitrogenous base, a sugar and a phosphate group.
A bit about DNA mutation for
Axis
the guy in the chat log. It's a simplification but it gets the point across.
The four nucleotides used in DNA are adenine, cytosine, guanine and thymine. For short, A, C, G and T. DNA is composed of two nucleotide strands in a helix formation, with these A, C, G and T bases pairing together. But there is order to the pairing. Only A can bind with T, and only C can match with G.
In order to replicate DNA, the strand of DNA must be split apart and then combined with free nucleotides to create a new strand. Because each base pair can only fit, literally and physically fit with one other type of base pair, you only need one strand to contain all the information. When DNA is replicated, an enzyme called DNA polymerase moves along a strand of DNA, splitting it apart. As the strands are being "pulled" apart, the base pairs bind with other, free base pairs in the surrounding nucleoplasm (like cytoplasm but in the nucleus). You end up with two strands of identical DNA.
A good analogy might be magnets. Say you have four kinds of magnets, but each magnet can only stick to one other type of magnet. If you glue the magnets to a string and then run them through a pile of other magnets, you'll end up with complementary pairs of magnets. For the sake of the analogy ignore the fact that there is no second string and ignore that the magnets in the pile would stick together. The actual chemistry is of course more complicated than that.
Thing is, the DNA replication process isn't perfect. Base pairs don't always match up correctly (the chemistry of which is beyond this discussion). DNA polymerase also functions as error correction, kind of moving up and down strands of DNA and correcting errors in them. We need this, otherwise we'd quickly degenerate into piles of...something useless, that's for sure. DNA needs to remain intact for things to function. However, even DNA polymerase isn't perfect. Sometimes base pairs will be mismatched, even after error correction. Then the next time
that strand of DNA duplicates, the result will be two strands of DNA, each with an incorrect base pair in its sequence. If you have an A that's stuck to a G, the resulting DNA strands will be AT and CG, instead of both being AT. These minor mutations are called point mutations. Normally they're harmless, because one base pair mismatch isn't enough to cause serious problems.
These mutations accumlate over time, through many generations. Enough of these may be able to produce a change in the physical traits of an organism. Many times these mutations are negative. A mutation might result in a smaller heart, reducing blood flow and physical endurance. Maybe the mutation results in a defective heart and the organism dies shortly after birth. But a mutation could also result in a slightly larger beak on a bird, or a slightly larger tail of a fish. This is where natural selection comes in. If the mutation results in a trait that is beneficial to the organism, the organism is more likely to survive, reproduce and pass on the genes to its offspring. If the mutation results in a trait that is determental, the organism will be more likely to die off and not pass on its genes.
Wow.

Bassoon, n. A brazen instrument into which a fool blows out his brains.