What Tom wisely points out is that one; there are many different types of dories, two the type has evolved considerably, incorporating many variants all called (many not rightly so) dory and lastly, that modern renditions of the dory are considerably different then the real dories that were fished extensively in the 19th century.
The 19th century dories, for the most part (all 15 or so variants) were heavily built by modern standards, though considered light in their day. They were also intended to "load down" uniformly, without ill handling or bad manners while bringing home a ton or so of fresh fish. These types, when lightly loaded are considered quite tender by today's standards, though an acceptable trade off then. These "antique" craft, should be left to those interested in preserving the type, because as sailors or pulling craft, they suck frankly.
Enter the modern dory or what is often referred to a semi-dory or modified dory. These are more skiff like in appearance, having less flare in the topsides, less height in the aft portions of sheer and most importantly a wider bottom beam to improve initial stability. Other features will include considerably wider transoms, compared to the tombstones typical of the antiques or the fat buttocked double enders. These "improvements" are a natural progression of the type and for the most part have changed them into a different breed.
If a modern semi dory (power version) or modified dory (sail) hull form is selected, for a designer familiar with the type, then you'll do well with your planned excursion/dive boat. If you elect to "doctor" up a conventional dory or a hull form that isn't well suited to your intentions, you may well end up with a boat that you just don't like to be out on.
Personally, I wouldn't select a dory for a dive platform. For this you want a boat capable of moderate deep water work, but a reasonably stable hull form. A dory, modified or not, isn't well suited for this. Weight needs to be kept very low in a dory, so out goes the cabin idea.
If working in the coastal gulf and other Florida waters, you'll want shoal draft, to go along with this stable platform. This means a much wider beam/length ratio then typically found in dories of any type. I'd recommend a Sea Sled design for ultimate stability, extreme shoal draft and lots of deck space for a house. If this shape frightens you, then a moderate V hull, with 16 degrees or less of deadrise. This will handle the occasional trips off shore, while still providing stability.
There are a lot of questions yet decided about your needs, much of which will help determine the hull form you need, such as the desired general speed, power train, percentage of time parked over a diver, compared to exploring the coastline, accommodations, equipment, budget, etc.