"January is the first month of the year, and February the second."
Translation:Januaro estas la unua monato de la jaro, kaj februaro la dua.
Also, at least in British English, "February the second" is a date, the second day of February, so it sounds better to repeat the "is".
I've definitely seen Esperanto sentences with the following pattern:
- Subject verb object, subject object.
- Mi vidas lian aŭton, kaj li la mian. (I see his car, and he (sees) mine.)
- Li helpas ŝin, kaj ŝi lin. (He helps her and she him.)
It looks awkward in English, but it's a bit more common in Esperanto.
Of course, you can leave in the verb in the second clause if you want to; there's nothing wrong with that.