Whatever source you got this information from is one you should no longer use. Rats will breed, and be healthy, at 12 to 16 weeks. First litters are often small and the moms don't always know what to do with the babies, but older females are just the same.
Your best bet is to find medium rats and raise them up a month or so, put them into your breeding groups and wait for babies. I often put a few males in with a group of females from the time they're weaned and just pull the girls as they get knocked up. Some go quicker than others. They go in with males in the 6 to 10 week range and do quite well.