Sleep in a different room with baby try not to be around dad too much (you or baby) sanitize and clean everything (Lysol the door knobs, toilet, couch etc.) when dad feels better make sure to wash the sheets and blankets.
Jabs don’t stop babies from getting colds. At that young obviously avoid infections but baby needs an immune system.
I suggest you sleep in one room with the baby and leave the dad on his own so you 2 don't get whatever he has. do not leave the baby in his own room tho bc he's too young.