This week's book giveaway is in the OO, Patterns, UML and Refactoring forum. We're giving away four copies of Refactoring for Software Design Smells: Managing Technical Debt and have Girish Suryanarayana, Ganesh Samarthyam & Tushar Sharma on-line! See this thread for details.
Why not iterate through each element in the original queue and check if the value is equal to what you want to remove. If it is not then push the same on to a different Queue. After the end of all iterations you ought to have a different Queue instance which contains all values from the original Queue except for the one that has to be removed.