Yes.
It's easy to do that. Just boot to your recovery system. Choose reinstall OS X. Select your external drive as the destination for the install.
When that completes, you will have a clean install of your macOS system. It will ask if you want to migrate apps, files and settings from your other drive.
Do that.
When complete, your SSD will have exactly the same setup as your internal.
NOTE : Before you begin this process, how much space is used on your present system drive?
You would have a 1TB hard drive, but if you have only used a small part of that, then you might use that amount to decide how much space you need on an SSD. For example, I have a mini with 1TB drive, but only about 80GB is actually used (really!). I think that I could get by with only 256GB for an SSD, but might get 512GB.
You may be able to do the same, unless the price of 1TB doesn't make a difference for you.