I think it depends on 2 things. First, what your definition of ready and second, what type of carrot you planted. Earlier this year I planted 2 types, Scarlet Nantes and Carrot Carnival Blend. I didn't keep track of when I planted them but I think it was about a month and a half, almost two months ago. I have picked 3-4 of them and they are what I think is a good size now for the Nantes but I think the Carnival Blend could use a little longer. The Nantes are short and fat and the Carnival Blend are long and skinny. If you pick them a little early, obviously they will be small, but they tend to be a little sweeter.

Edit: In pulling a few more carrots out of my own garden I realized that the amount of leafy green showing above ground is a good indicator of the size of the carrot below ground.

Thanks! The sweetness is definitely interesting. I guess I'll just have to probe them regularly.