Is the intention to eventually get rid of the old domain/brand (provided that the new one is successful)?
Duplicating a domain would mean that you would pay extra for PPC (driving different brand terms) and would also mean that the reskinning would include some brand-term landing pages.
I don't think your new site will take off from an SEO perspective - especially considering that it will take about 4-8 weeks for the index to properly build out and you will only know about any duplicate content issues after it happened.
I think "trying out a new brand" is a bit dangerous, by just duplicating content on another domain and slapping a new skin on it. Unless of course the current domain does not have much SEO value with regards to branded keywords.
Depending on the number of products I think it would be better to pull up the new domain with a set of landing pages (preferably covering some of the most revenue-driving and least revenue-driving products) and a set of product pages with canonicals to the new domain and sitemap for the selected set of products and then setup PPC and funnels and do a side-by-side comparison.
If the new domain/SERPs/conversion performs better, 301 the old domain to the new one and move your products over. Anything else feels like being half-pregnant 