Unless you have plenty of time don't bother with a questionnaire. Go around and talk to the staff, teaching and support staff. Get a feel of what they think is lacking and what they would like to see. Most of which you probably know anyway but still ask them, this will make any transition easier later on because they are aware of what you are trying to achieve.
As for the DP itself - start by explaining what you have in place and why it should be replaced or updated. Start from the switches to the servers, on to the clients, IWBs, projectors, printers and software.
Don't forget to mention things that the user does not see such as backups, filtering and Anti virus.
Then create a step by step plan on what to do to put it right, but do it in a way that a non IT reader can understand the basics of what you are saying. For example when I arrived here there were hubs instead of switches, so I gave a brief explanation as to why switches were better and why they should be given priority over new PCs etc. I them moved to the servers and so on. Eventually you get to a point where you are actually creating a 5 year plan at the same time.
I suspect money is tight, so break it down into sizeable lumps which could be spread over a number of years (5 year Plan). The management can then see what needs doing, why it needs doing and what the costs are.
The more effort you put into this first plan will ease the pain in future years as you already have a base to work from.
I might still have a copy of the first one I did here, obviously out of date but if you want a copy, just let me know.