How can I improve the baking of frozen cod and rice with carrots,?
You're not going to get any browning on the vegetables.  By cooking everything together, you're steaming everything, preventing anything from browning.

If the carrots were on the top layer, you could put it under the broiler (top heat)for a minute or two, after everything's cooked through ... but for that, I would put the rice on the bottom, the carrots above them, then the cod.  Cook to your normal doneness, remove the cod and broil until you get some brown on the top.

You might still get away with it if the rice and carrots are mixed together -- there's a special name for the layer of crunchy rice that you get when cooking paella which adds flavor and a contrasting texture.

As for flavorings -- garlic and onion would have been my go-to in this sort of thing ... but I'd also add bell peppers, possibly roasted in advance.  For spices, I'd serve it with za'atar blend -- the citrusy quality of the sumac helps to brighten up dishes.

If you don't have za'atar (most people don't), you could squeeze over a bit of lemon juice, or sprinkle some vinegar over it (but something that tastes good on its own -- apple, wine, etc ... not white).  Tomatoes can also help -- but if it's out of season or you only have grocery store tomatoes available, go with canned tomatoes.  (canned diced are the easiest for this sort of thing)

Another option is to finish the dish with some fresh herbs -- flat leaf parsley, basil, oregano, thyme or culantro might go well with those flavors.

As for recipes -- I'd look at paella recipes -- although it's often cooked with only bottom heat (on a grill or other burner), if you have a suitable shallow pan, you can start it on the stovetop (to brown the carrots a bit before adding liquid), finish assembling, then put it in the oven to finish.