opportunity to restructure a department

There is no one answer fits all for this scenario.

Normally a restructure occurs because of changed mission, gaining economy of resources, alleviating workflow bottlenecks, consolidating redundant services, etc.

You need to apply the basic problem solving steps:
What problems exist in the current organization?
Do the problems relate to the organization or something else?
What are the possible solutions?
What solution(s) make the most sense economically, politically, culturally, etc.?
One thing you can use to help you make the right decisions as far as staff, is statistics captured during current operations.

For each separate area you currently staff:

Is the staff consistantly over or under worked?
If overworked, how much of a backlog is there? Does the backlog ebb and grow (normal)? Is it consistant (got behind, can handle the current workload, but not enough time/people to make headway on the backlog)? Is it constantly growing (will never get caught up without more people)?
Is the backlog truly a product of too much work for too few people, or is it a product of inappropriate/insufficient skill mix?
What roadblocks/bottlenecks exist? Can they be alleviated with changed processes vs. changed organization?

For a help desk organization:
What is the skill level of help desk personnel?
What is the average user skill level?
What is the average duration of a help desk call based on complexity of the problem?
Are there common, recurring help requests that could be alleviated through proactive user training?
What is the complexity of the software/hardware you support?
Do you support proprietary and/or inhouse- developed software/hardware?

For development environments:
Are development projects for internal or external customers?
How thorough/consistant is the requirements development process?
How well is project "creep" managed?
How accurate are timeline estimates?