How to get SQL Server Developer edition for installation in non-production for the organisation
Licensing questions are generally not applicable to this forum, but this is a pretty high level one that's more about process, and for an edition that technically doesn't require paid licensing.
Developer Edition is freely available right off of Microsoft's website for SQL Server. The direct download link is here. This will be for the latest version, 2019.
From a process perspective, you just need one copy of the installer and your company's System Admin should be able to use it to install Developer Edition on all of the servers you need to test with.