It's okay for there to be two tonic chords in a row, especially in the beginning. The main point of the beginning (and ending) of a piece/passage, at this point anyway, is to establish tonic, and considering the fact that the piece starts on an anacrusis, it is not unlikely to have another tonic chord on the downbeat of the first full measure.
As far as it going to a ii chord though, that is not your only choice, in my opinion, it could also be a vii'6 chord, going from I-vii'6-I -- which is not strange at all in my current world, that is considered to be a "tonic expansion" by way of a chord pulled from the dominant area. So, okay, going to the first fermata (which is a V chord, meaning we end there on a half cadence), a potential chord progression that I come up with is I-I-vii'6-I-I-vii'-I-V. You could replace vii' with ii in the first potential questionable one, but as far as it "needing" to "resolve" to V, I am not sure what you mean there.
Voice leading and tendency tones may help to determine here. 7 is supposed to resolve up to 1, and 4 down to 3, no matter what chord they are in, I believe. 7 isn't in the ii chord, but the way this is written, if you use the vii' chord, scale degree 7 could be written in an inner voice and resolve as it needs. The problem is that no matter what chord you have there, the soprano "A" is "supposed" to resolve downward to G#, and it doesn't in the first example (but it does in the second one). If, for some reason, using a ii chord means you don't have to resolve the scale degree 4 down to 3, then I guess you have your answer there (I will have to check on that, I guess).