In my personal view, yes you are transporting the fish, but you are not placing them in another body of water..
I look at it as you using your Aquarium as a "holding tank/livewell" but they would count against your limit since
they are still living. I would go by the daily limit for which your house resides in the zone. So if you limit is
say 50 crappie and you have 5 crappie in the aquarium.. If you go fishing down the road in the same zone, your daily
limit would be 45, as you technically have 5 still alive in your possesion at home.
I have never came across any law about transporting live fish from one body of water to home, as I prefer to keep the
fish alive as long as possible until I am home to clean and package them.
If it was against the law to keep fish alive in your livewell, with your boat on the trailer.. I think there would
be issues with all Catch and Release fishing Tournaments.. As the fish are placed in boxes to be kept alive to take ashore
to the weigh station before they are released back in the water.
As for the fish being kept in a aquarium and not having much color, its due to their surroundings. if you place bright objects
and plants in the aquarium and there is lots of natural light in the room they will stay bright.. Its just like camo, most fish
adapt to their surroundings.