I got the impression that her mother gave her *both* poems to memorize; she just had trouble with the one and no trouble with the other. Also, if you read the actual poem, it has a big moral at the end, just the kind of thing that adults would give children to memorize in those days. I don't know, but I suspect that all the poems JA mentioned in ch.1 were quite well known at the time, because they were considered among the canon of "instructive" poetry of the era, so schoolgirls all over England would have learned them.

Also, I don't think Catherine was consciously "training" to be a heroine. IMO, JA was just having fun with the idea that Fate or Destiny (with a capital letter) were preparing our heroine for what was to come by making sure she learned the right poetry. ;-)