Can somebody travel outside the US for a short trip if they are on a K1 visa?
Unfortunately the K1 is a single-entry visa. This means once you enter through a port of entry, it is essentially useless. It does not allow you to leave the country and re-enter. It's best to avoid leaving the country while on a K1 visa. Technically you could apply for a travel document (advance parole), but by the time you get it, your K1 visa will likely be expired anyways.
The conventional thing to do in this situation is to apply for your adjustment of status and get your green card. Then, you can come and go as you please. When you apply for your status adjustment, you can concurrently apply for employment authorization and travel document and there's no additional cost or filing fee when you file that concurrent with your adjustment of status. When you use RapidVisa for your adjustment of status, we include this service.
Once you do this, you'll receive a "combo card" which combines your employment authorization and your advance parole, and then you can travel all you want while you wait for your actual permanent resident card or green card.