The trick I usually do in such cases is to send the object serialized (with Storable freeze) through the queue. That, obviously, means the objects represent more a IPC then actual memory sharing, but you didn't give enough information to know if serializing the values is appropriate.
Note that threads in Perl are not like threads in C, or Python, or Java. In all those languages, all threads share the memory with every other thread (note that python gives up real concurrency to do that). In Perl, you can only share specific data. And there are a set of limits on how the shared data should look like.
This makes threads in Perl unbearable for a lot of scenarios, others simply get much harder, but the bright side is that Perl has real concurrency (while Python has a Global Interpreter Lock). But usually, in Perl, when you want to use threads, you really have to design your app with that in mind, you can't just parallellize a small part of the code.