Just to correct the record... gelcoat resins are NOT finishing resins - they cure with a tacky surface to allow the application of the laminating resins over the top. Because of this, they can give off styrene monomer stink for a very long time. If you want a heavy-bodied polyester resin, as a finishing coat, get a 'flowcoat' resin. It sets up with a hard surface and is designed as a final coating.
I presume you want a relatively easy way to seal the timber, with as few materials and steps as possible. Epoxy is still the best product for what you want, along with the pourable product that Swampie suggests. I was assuming that you will work in a very well ventilated area, wear protective gloves etc, whatever product you choose to use.
Don't be casual about the mixing ratios of whatever you use either - don't just 'mix a bit of this with that..." the space your animal is living in is enclosed and relatively poorly ventilated, and probably heated as well. You need to be sure that the various components in the mixes you use are fully used up in the reaction as the resin hardens, or the surplus compounds can 'outgas' for a lot longer than you want. It's not rocket science... anyone who uses these products regularly can help. The thing you need to consider is that this is the living quarters for your animal, not a boat or some other item that is outdoors in the weather.
Another thing worth knowing, exposing the painted surfaces to sunlight greatly accelerates the curing of most of these products, so placing the painted components or enclosure in the sun when you've finished applying will set it up very quickly. Just don't mix and apply in the sun - it'll set up before you finish applying it!
Jamie