This is a very good idea and please pursue it. You should look at people who have tried similar things and the problems that they had.
The main problem is once the pressure goes above 1/2 atm the boat wants become spherical or at best a cylinder. This is not a good shape for a cat. You can fix this if you put in stringers, bulkheads or something similar to make it hold it's shape but this adds weight and cost.
The other major problem is that even at 2 atm an inflatable structure is still relatively flexible compared to rigid structure of the same weight. Again this is not good for a cat.
There have been a couple of tries at solving these problems. One solution involved inflating a double walled skin instead of the whole structure. The area between the skins contains something like a low stretch open cell foam. With this you end with a structure like foam core fiber glass. There was even a proposal to inflate kevlar open cell foam to 100 atm. I have heard a couple of stories about this and they all say you can do a lot of damage if it fails
One of the big inflatable companies Avon or Zodiac or ? had a report on some of things they had tried and their results
Most of the work on building better molded plastic structures have been by other industries (auto, aerospace, toy etc). The two major areas are a better technique and a much better plastic. .
An example of a better technique: First you mold a thin hard high melting point outer skin. Then you add a lower melting point (so you don't effect the skin) foam for the core. Last you add an even lower melting point inner skin. The big problem with this is making sure the layers bond together.
A much better plastic: Most these involve a post molding cure. After you finish molding the boat you subject the boat to a special temperature, pressure, gas, liquid, etc and the plastic turns into a light weight high strength material. An example of this is converting rayon into carbon-carbon. So far these are really expensive.
Please continue looking at this, but look at what other have done so you don't repeat their mistakes.