January from nine months doesn't really fit into the kollel schedule. You'll catch the last half of winter zman, Summer and Elul.
Not sure what your goal is with this but IMO by the time you get adjusted it'll be time to leave.
And I doubt anyone will be interested in employing someone who has no experience for nine months. Not worth the investment
Something else to consider...instead of going from January to after chagim, there are many reasons to go from chagim to tisha b'av.
1. Kollel schedule, chavrusas, new place..you will be coming in the middle of the zman - nisht here, nishte heir. After pesach to summer is short and much more shvach. Summer zman can be really shvach in American yeshivas because of everyone coming and going. You'll be ending with Elul, yeah!, but your heads will be in packing and leaving by then. If kollel is your entire morning/day and you don't find your place, then the effort is almost for naught.
2. Elul time is so geshmak in a good yeshiva; it can carry you through for months!
3. You'll be starting at the same time as everyone else!
4. The chagim and especially succos is a time for inviting. This is a PERFECT opportunity for all your new neighbors and contacts to invite you for meals and you and your wife can exponentially immerse yourselves in new social relationships. This will make it so much easier for you two to be more quickly socially integrated.
5. I imagine any work opportunities for you and your wife would be more available in Elul, beginning of the year, than in midyear January.
6. Your daughter would find and start a gan with everyone else as opposed to coming in the middle of the year and hoping for an opening and expect instant acceptance to already formed playgroups. (Of course, it's possible, just easier when she starts with everyone else.)
7. You'll have all the reasons #1-#6 above all over again when you come back to America after Elul at the end of your 9 months. Better to come after Tisha b'Av to allow yourselves to prepare for the new year in kollel, work, school. If you are planning on working PT with schoolage children, jobs go Sept-Sept.
IMHO, to make your dreamtrip come true the way you envisioned it, it makes more sense for it to be from Elul or at least from the chagim to summer instead.