My oldest son is now 5. He was right at 18 months old when we got him his race car toddler bed, because we were moved and thought why not set up his new room in his new house with the new bed? He loved it, and stayed in it until he was 4 1/2 actually. Maybe he's shorter than some? Or maybe because the race car bed doesn't have rails it's not as "confining"? I dunno....because he was just fine sleeping in it. We could tell the day was coming, but he hadn't outgrown it yet, at 4 1/2.
We moved into our new house at the end of June and our youngest son was almost 19 months old and was getting too big for his crib, so that's why we moved them to new beds. I bought my 4 1/2 year old a great bunk bed and set up his room cowboy stuff so he was amped about his new room and new bed again. I painted and decorated my 18 month old's room and gave him the race car bed which made him very proud. I think that putting an age on something is a little bit of a mistake, especially if money is an issue. I would definately start saving and preparing for a real bed now, but your child doesn't "need" a "big bed" until he's "needing" it, if that makes any sense? When your son is too tall for the bed, he needs another one.
As for fear of the "what ifs" on if he falls, I would suggest a couple things: first you can get a rug at Target for pretty cheap to put by his bed, and that might be more pleasant anyway so his feet aren't so cold when he first gets out of bed. What I did for my guys when they first started sleeping on the toddler bed was lay out the stuffed animals on the floor beside the bed (I was thinking that if he fell and landed on Tigger, Bob the Builder, and a few bears it'd be nicer than landing on the floor). Babies R Us (MAYBE Target and Walmart, but for sure Babies R Us) sells safety rails so it's like a toddler bed, for real beds. You stick it under the mattress and pull the thing up and lock it. I didn't do that though, since my son's twin bed is actually a bunk bed shaped like a T, so there's the back of his dresser on one side, and the book shelves on the other side, so he'd be "held in". I was really happy with that arrangement, and I bought this bunkbed, with a dresser, bookshelves, headboard, 3 drawers under the bottom bed, a desk with drawers, a built in bulletin board for his desk, and a removable ladder, with mattresses, for $200 on craigslist. Craigslist can hook you up with some great deals! Of course we threw away the mattresses because I didn't want a used mattress, but we got an inexpensive one during the Memorial Day sale and he slept on that for nearly half a year before we gave him another mattress for the top bunk and put the ladder on the bed.