I ate a vegetarian diet for seven or eight years, a vegan diet for a few months* along the way, and have had a primarily* * vegetarian diet for years since then. I give blood regularly (I'm AB+, a rare donor blood type), and I've never, ever, ever had a problem with low iron - it's usually been quite high. While that's only one data point, it seems consistent with what I've read about nutrition - problems mostly occur when people give up meat but still eat a rather monotonous diet. ("In other news: Eating nothing but twinkies and whiskey is bad for you...Film at eleven.")
* I'm a cooking geek, and was interesting where those constraints would lead me.
* * same, plus fish and occasional Italian and French/Vietnamese charcuterie (Bánh mì!), but I cook/eat vegetarian by default.
hence, you should have no trouble. :)
Besides: Lentils, spinach, and broccoli have iron. How many vegetarians don't eat at least one of those regularly? (Other cliches: vitamin B-12 - Vegans might have a problem, vegetarians are fine. Calcium - "Dark green leafy vegetables". Do vegetarians eat those? Oh. Wait...do carnivores eat those?)
This is, of course, because fish is just a specific kind of meat, so nutritionally it's not vegetarian in the slightest.
For years I was a vegetarian + fish guy. I hate pork, my family boycotts lamb, and I didn't have a taste for beef. Nowadays I eat the token hamburger every few weeks, because I've noticed I feel a lot better for it.
That being said, there's usually a vegetarian meal in every box of MREs.
Also, the whole vegetarian "protein deficiency" thing has been pretty thoroughly debunked, unless you only eat potato chips. It's surprisingly difficult to eat a diet that won't give you at least a minimum of protein without dying from e.g. pellegra or beri-beri first. (Maybe not enough protein for hardcore bodybuilders, but certainly enough to live well.)