With a C+ support the level requirement to recruit Catherine is only 9. You can unlock the C support by sharing two meals with her and giving her the whetstone from one of the earliest monastery quests. Sharing two more meals with her after viewing the C support will give you C+.
Note that both participants need to enjoy the meal for it to yield the required support points, and that "today's special" gives around half of the support points.
She is not deployable in chapter 4, so there is no need to recruit her that month even if it is possible. Including her in four meals before starting chapter 5 is not a big investment considering how good of a unit you get in return. IMO she is one of the best units in the entire game on maddening due to her early game contributions (with Blue Lion and Golden Deer that is). By recruiting her this early you can also learn her class mastery skills such as Death Blow and Hit +20 to increase her long-term potential, or alternatively make her a Pegasus Knight.