I assume that you already evaluated and rejected the similarly-named GD::SVG, which does implement the copy method (but not clone, copyMerged, etc.). (I've never used either, so I don't know the merits of one over the other.)

You might want to try to roll your own sub SVG::GD::Image::copy { ... }: create the initial image with SVG::GD::Image::new(); use Data::Dumper (or similar) to get the details of the SVG::GD::Image object and find all the attributes/data that are important to you, and copy those attributes from the original to the new. I think you can just define it in your own code using the fully-qualified package:: name, but if not, put it in your installed copy of SVG/GD.pm (assuming you have write privileges).

Once you've got it working, you can send it to the maint of SVG::GD as a feature request; having written the code already, it's much more likely to make it in. :-)