Is a PhD in a small university in a small country restrictive for an academic career abroad?
This is important career advice and should be given by someone who you trust who knows you personally.  If no one comes to mind, ask your existing professors in the field.
As you suspect, there are powerful reputational and network effects from prestigious programs.  It would be hard to argue that your employment prospects after graduating Cambridge are fairly good! You have heard of it and respect it. Your question is - how does your future employer feel about your Uni?  Have they heard of it? Do they respect it? Do they teach what you want to learn?
The question is very specific to your field.  Perhaps your Uni is universally known for the subject, or has undeniable geographic advantages - like studing Marine Biology at U-Hawaii or being across the street from CERN. It is hard to tell how strong that reach is until you have dipped your toes in the job market.
Note: while you can trust your teachers to guide you honestly, do not expect them to talk poorly of their current institution to a student. They will not.  Simply be aware that if the local institution &quot;is good enough&quot; is not the same as saying &quot;we are one of the top institutions in the world, of course you should stay.&quot;