Yes, this is an excellent example of where MSMQ makes a lot of sense. You can offload your difficult work to a different process to handle without affecting the performance of your current process which clearly doesn't care about the results. Not only that, but if your new worker process goes down, the queue will preserve state and messages (other than maybe the one being worked on when it went down) will not be lost.
Depending on your needs and goals I'd consider offloading the download to the other process as well - passing URLs to work on to the queue for example. Then, scaling up your system is as easy as dialing up the queue receivers, since queue messages are received in a thread safe manner when implemented correctly.