This is gonna sound like one of FR's posts in the monitor forum, but here I go.
I can see you have purple sand, or something that looks like it, as your substrate. Big no no. Iguanas are tropical animals and live in rainforests. There is no sand in the Neotropical rainforest. Trust me, I've been there and seen wild igs. You need something like cypress mulch in there. (Not bark chips, they suck for ALL herps)
I REALLY REALLY hope you realize what youre getting into. From now on, you or your wife should NOT give animals as presents. The animals are almost always not researched and impulse baught. This situation is very common and I REALLY wish no one sold iguanas. In a perfect world, people would need a license for big/dangerous herps no matter where they lived, pet stores would not sell animals, only supplies, no animals would EVER be wild caught for the pet trade, and breeders and shows would be the only way to attain animals. But thats gonna be awhile. People buy the cute baby ig and put in the absolute worst care and never do ANY research. They end up dumping or releasing their ig when it turns into the 7 foot nightmare of a lizard and its a lose-lose situation. Iguanas are VERY expensive to keep. The massive enclosure they require and the many basking lamps, cost of food, electricity bills, and all that will drain your wallet. So be prepared.
About the gender, you were partially correct about the mild temper indicating a female. This only applies when they are mature however. You WANT your ig to be a little feisty when young. This shows it is healthy. The females, when mature, are much more laid back (and smaller and easier to keep). You can only tell which gender it is once it gets to subadult. The females have a smaller head, a smaller dewlap (I dont know about the dewlap notch thing, never heard of it.) and will be on the calm side. Males get massive pores when adult and they secrete a waxy substance to mark their territory. Female pores remain small, but now is to early to tell. Males will have a much bigger head and dewlap. Males, when mature, are a NIGHTMARE for the begginer keeper. They get HUGE and are very violent during the breeding season. They will turn bright orange and become VERY aggressive. I have seen male igs that have removed fingers. Be VERY careful. But they act as calm as females during the rest of the year. If you want to see a big dominant male in breeding colors, look for one of sideman17's posts. He has a massive, beatiful male named Dexter. Dexter the picture of iguana health. ALL male igs should look like him.
Anyway, he/she looks reasonably healthy but should be slighty fatter and should be bigger for a 5 month old. Petco has a way of lying, cheating, and starving their animals, so this is not your fault that it is smaller than it should be. Your ig is Wild Caught (WC) and should be taken to a REPTILE, not dog, vet for a check up. Any WC animal should be taken to a vet straight away.
And you said you carry it around town inside your jacket! Dont do that! There are soooo many things that could go wrong there. It could escape, suffocate in your jacket, get stolen, have a panic attack, etc. The iguana only wants to be left alone in its cage. Handling is ok as long as its indoors and not for too long. If you absolutley must take him outdoors, buy a harness that wont damage his spines (some of them can hurt the ig, be careful) and wait till hes bigger, about 4 feet, to take itout. It will be more used to and will be easier to keep track of when bigger.
Here is a wonderful link for igs. Mellisa Kaplan has the most ig info on the net. ANd Ialso reccomend the book Green Iguana- The Ultimate Owner's Manual by James Hatfeild. Its about 20 bucks and is the absolute BEST source of ig info ANYWHERE. I'm terribly sorry if I offended you, but I'm telling like it is and I really want best for your little ig. Next time, stick with something a lot easier and research your butt of
BEFORE you get it. If you have any questions, feel free to ask here! Trust me, that book is a MUST HAVE for any ig keeper and you NEED to bookmark that website. Good luck with it! 

Link