This can be a bigger job than a lot of people realise, You should not lose any traffic assuming you do everything correctly. 301 every page to the corresponding page on the new domain. Track down every reference within the site including assets and make sure they all point to the new domain. Make sure all the canonical tags are pointing to the new domain. regenerate any sitemaps you may have etc.
Once everything is in place I would run screaming frog across the site to confirm every reference is removed.
The one danger you have is creating redirect chains. Your new site should not contain any 301 redirects, only your old site and they should goto the final page. If all this is done then traffic will flow and any traffic lose will bounce back over the coming weeks, it can take time though.