C.B.
3 of my kids have been anemic between 9mo and 15mo. Are you using a supplement? The one that we have found to be most effective is called Ferrets IPS. It is a liquid with a flavor, so it is much easier to give to little ones, and it doesn't bother tummies like so many other iron supplements do. It is not a prescription supplement, but it is not typically just sitting out, so we did have to ask the pharmacist for it.
Having worked with the same pediatrician with all of my kids, we have worked together over the years to more efficiently treat the anemia when it does happen with my kids. One thing that he learned when my most recent anemic baby was having issues was that pomegranate juice is loaded with vit C and really makes a difference in the iron absorption. It's expensive, so I bought a bottle and then froze it in ice cube trays and would just melt one of the cubes and give it to my son immediately following the iron supplement. Though he was the most anemic of any of my kids, he came out of it the fastest, had the greatest level of recovery, and began gaining weight again faster than any of them. I really think the pom juice made a difference!
It isn't just dairy that interferes with iron absorption, it's calcium. So if he's drinking calcium fortified OJ, that will be just as much a problem as drinking a glass of milk as far as blocking the iron.
Don't worry too much about meat, there are plenty of other iron rich foods out there that toddlers tend to do much better with. There is a decent list here: http://www.fatfreekitchen.com/nutrition/iron.html, although it you just google "iron rich foods" you should come up with a number of lists.
GL!