Copying of DNA followed by mutation has of course happened in real life and lead to the formation of new genes. My favorite example is the sdic gene is Drosophila melanogaster.
"The gene was created from duplicatedand hence dispensablecopies of the genes for annexin X (AnnX) and the cytoplasmic dynein intermediate chain (Cdic). Three large deletions led to the fusion of the duplicated genes, whereupon a series of smaller deletions and nucleotide substitutions fashioned a new amino end of
the Sdic polypeptide and created motifs characteristic of known axonemal dynein intermediate chains. The regulatory region of Sdic,including a spermatocyte-specific promoter element, also evolved from AnnX and Cdic sequences"
(Chromosomal Effects of Rapid Gene Evolution in Drosophila melanogaster, Dmitry Nurminsky, Daniel De Aguiar,Carlos D. Bustamante, Daniel L. Hartl, SCIENCE VOL 291 5 JANUARY 2001)
so the creationist information argument is not only false in theory but in practice as well.