I'm not sure what to expect at a year because my DD is only 10m too. But I went back to work a couple of months ago and she has been fine about having cups of formula or EBM during the day in my absence.
DD clearly associates breastfeeding specifically with me. If I'm not around she'll happily drink from a cup. If I am she doesn't see the point and just grabs at my top excitedly instead! It is pretty cute when she toddles over to pounce on me when I get in the door from work.
It may take a few days for your DS to adjust, but he will. And a good carer at nursery or childminders will understand this and allow lots of time and cuddles whilst he gets there.