I would go ahead and transplant, now! If they are in that peat pot, I tear that off and throw in compost, or back area of yard (it does break down).
I would put both in one pot, at least 12" diameter. Both thyme and oregano spread and fall over the edge of pot, very pretty. Keep them outside, and you may not have green all winter, but the new green will show pretty by Feb-March.
Just throwing in one of my little things. I might have a pot 14" or so. Have the thyme and oregano on 2 points of triangle, and put in chives on the 3rd. It grows up and gives a nice visual dimension.
You didn't say what sun you are keeping them in. Especially where you are, an eastern (AM sun) may be best (over all day).