Hi David,
Largesarge is correct, there is a lot of information on the Geotech forum and there is a lot of information on this forum also about coil building. You just have to look for it. It won't jump out and come to you.
Now, I doubt you will have anyone answer your request to build an odd size/shape coil. Just the cost of the housing can become prohibitive, let alone any forms needed to wind the coil(s).
So, you will probably have to build one yourself if you want a special size. That is why I recommended you start by using a housing size that is already available. This solves a large part of the battle of coil building. By using a housing that is already available, you have a better chance of getting someone to build a coil for you if you still do not want to tackle it yourself.
Should you decide to try it, you will need to know the number of turns and size of the windings needed to match a desired inductance. However, you need to know the inductance that you want. I would select about 300 uh to 350 uh to begin with. Since the coil you want is going to be large by normal standards, 300 uh would probably be best. This will allow the coil to work at the shorter delays. Now, if you want something as large as a 5" by 18" coil, then you probably will not be able to get it to work at the shortest delay setting. It will be tough, especially for a beginner. On the plus side, this housing is available.
Next, you have to decide just what type of coil you want, a DD or a mono. A mono is easier to build but more difficult to use over the ground since it is much more sensitive to ground minerals. So, for a GQ, I would recommend a DD coil.
Next, you will have to decide on the wire type to use in the coil windings. Then you have to decide how to lace the windings tight. Using something like spiral wrap is a good choice. Then there is the shielding and just what to use for it.
Of course, now you will have to track down the proper wire for the coil lead and then find the proper connector.
Finally, there is the coil assembly and decisions as to what type of filler to use, foam, epoxy, resin or some other material.
Many of the answers to these questions can be found on this forum or on the Geotech forum. Once again, the GQ is very forgiving and as such, about any wire size or type can be used. However, some do work a little better when trying to make a faster operating coil.
This is just a basic layout of what is involved. Is it complicated? Yes and no. For a beginner, it is quite complicated and easy to make minor mistakes. However, the GQ is very forgiving so any error will simply result in the coil not working with no harm to the detector.
Can it be done? The answer to this is yes. It will simply take some time and a little more knowledge of what is involved. Can you find someone to build a coil for you? Maybe if you are a little more specific and willing to accept size housing that is available.
Finally, you should be aware that most large coils will probably need to be "matched" to the detector to assure it will work at the fastest delays possible. Since this may not be possible, then you should expect that a large coil will require you turn the delay up to work properly.
Reg