Without writing custom code (as per your comment on Aviram's answer), it is not possible to achieve the exact same thing, but nonetheless it is possible to achieve same effect;
You say that a 'source queue' distributes messages to other 'separate queues' according to a custom JMS property. I'm assume that you have MDBs (message driven beans) configured to process messages in these separate queues.
What you can do with WebSphere is distribute messages to these MDBs directly from the 'source queue', without having to filter/distribute them to separate queues.
This is managed by using JMS Message Selectors. You can point all your MDBs to the source queue using activation specification definitions, and for each (one for each type of message) MDB, define a JMS Message Selector that matches the ones you use in WLS. This way each message is only delivered the MDB whose filter matches the message's properties. This effectively filters/distributes messages to different MDB's as in WLS.
You may read details on configuring message selectors (during development in RAD, or at/after deploy time) at infocenter. Below is a quote to give you an idea about what it look like;
messageSelector
This attribute determines the JMS message selector
that is used to select which messages the message-driven bean
receives. For example:
JMSType='car' AND color='blue' AND weight>2500
The selector string can refer to fields in the JMS message header and
fields in the message properties. Message selectors cannot reference
message body values.