For me ( I loathe big changes) I would be very very proactive. Start calling now to set up appt for Pdoc , T , GP etc .. maybe you won't like one or all.. But getting your foot in the door is always best.
I would also start looking for possible groups you can join, what is there to do or see in this new town, I personally would find the first coffee shop I could, Coffee shops are comforting to me like bookstores also. What free activities are available? Meetups? Certainly having a dog can complicate moving , but... look into dog parks? Where are good places to take your dog for exercise?
Moving is always stressful. Buy some ugly dishes at a thrift store and when you just cant stand it ,, take one out and smash it.. Its helpful sometimes... I tend to put mine in a plastic bag so clean up is easier.
Find ways to let stress out daily , If its allowed to build up the explosion level your going to probably get flung into some sorta Bipolar hell .