The cage size is adequate for a few more months, but he should really be in a cage that is one and a half times longer than he is and as tall as he is long.
Igs are easy to get (cheap) but are surprisingly compicated to keep healthy and happy. The main areas that need to be just right are cage size, diet, temperature, UVB light, and humidity.
I'm glad you mentioned his diet, because it's not quite adequate. Carrots are not very nutritious and have oxalates, which is a nutrient that robs iguanas of dietary calcium. It's the same with the kale. You can feed 1/4 cup of kale per week, just to add a little variety, but too much is not good for him. the main diet for a captive United States ig should be turnip tops if you can get them, collard greens, mustard greens and dandleion greens. One grocer in my town special orders a case of turnip tops for me, once a week; very inexpensive. Add to the greens shredded sweet potato (yams), shredded winter squash (acorn or butternut are two), and sherdded parsnips. Your ig will get used to these new foods and learn to eat them, and be much healthier for it. My statements about diet are in line with all the up-to-date information sources. Check :
http://www.greenigsociety.org/careinfo.htm
He *needs* proper heat in his enclosure to be able to digest his food. the best diet, without proper heating, will do the ig no good. All igs need to have a place in their enclosure to bask at 95 degrees, which stimulates his gut organisms which break down the vegetarian diet into nutrients his body can use.
He needs to be able to move away from the basking area to a cooler area that is in the 80 to 85 degree range. Igs' bodies tell them how and when to bask. You will probably need a four foot long cage to get those two temperature zones. When he gets larger, he'll need a cage that is 6 feet wide minimum.
A problem that can stunt ig growth is gut parasites and bacteria that are bad for hem, They bring these organisms with them from Latin America where they were hatched. A vet visit for a poop exam finds those harmful gut creatures, and they are easy to treat. Once he is free of these infesting bugs he will be able to put his nutrition into growing and not into fighting the infestation. This is a *very* common problem with iguanas, and experienced ig keepers take their new igs right in for the poop testing.
Igs need thir skin to be exposed to UVB light. UVB cause a chemical reaction in their skin that lets them build bone with dietary calcium (that is a simplified explanation). They need either several hours of warm midday unfiltered direct sun exposuer, or they need light that puts out UVB in their cage. These lighs are expensive at pet stores ($40) but are cheaper from on-line reptile supply stores ($15 - $20). See www.LLLreptile.com which is just one of a dozen or more online reptile stores.
Without UVB, an ig will stop growing and get the disease called Metabolic Bone Disease, also called Rickets, within six months.
I hope I didn't give too much information. But it's all necessary for your ig to be healthy and to thrive.
Happy herping,
roger