Depends on the purpose of the code.

I think the first is the cleanest way for simple loops of this sort, and I'm reticent to use infinite loops for anything other than long running processes. Setting up a deliberately short-circuited infinite loop for this kind of purpose can work against intelligibility IMO. Labels I use semi-frequently but only in nested loops and switches.

Here's some fun code though:

use Experimental::Exception;
do {
.....
} while (
         try {
           $thingy->doSomething();
         } catch SomeException => sub
             { 
              return undef;
             }; 
         )
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