Rice cereal is fortified with iron as you say. Breastfed babies are born with enough iron to last them for a
minimum of 6 months. The 6 months thing is often cited as some baby's own iron reserves from birth run out from 6 months but for some these stores last up until 12 months. Breast milk contains less iron than other baby milks but crucially it is very 'bio available' and easy to absorb so ends up being an excellent additional source. Babies on formula receive iron there too.
Babies receive iron stores from their mother in the last trimester of pregnancy so premature babies who have missed out will probably need additional sources of iron from 6 months for sure. Babies who were born light (less than 6 pounds or so) will also need iron in their diet from 6 months as it seems they receive less stores too.
So around 6 months is a good time to start other sources or iron to be extra safe but studies have shown babies delaying as long as 7-9 months have been fine. Some parents who wish to delay solids for health reasons have blood tests for their babies to check on iron stores. Babies as old as 12 months with only breastmilk as a source have been shown to show no signs of anemia. However I'm not saying 'let's all wait 12 months' - these babies had a family history which suggested a longer delay before solids or health problems themselves. Sometime around 6 months is a good starting point but of course cereal is not the only source of iron.
Sweet potato and squash are also good natural sources of iron. Also prunes, spinach, brown rice, dried fruits, meats.
For iron absorption to be most efficient it is good to combine it with sources of vitamin c.
So after all that waffling
I'd say if you're baby was light or premature you may want to pay particular attention to sources of iron from 6 months. But even that doesn't mean cereal for sure. Most babies who begin solids will be firmly established on a diet containing iron sources by the time it's an issue.