Well the answer is yes and yes. Leaving the wine for 13 months, and THEN oaking it is the problem. Oak extraction is best performed either during secondary fermentation, or as soon as the wine is stabilized. In wineries, it is placed in oak as soon as it has stabilized and cleared, then tested at intervals until the desired amount of oak is present. Once that has been reached, it is withdrawn from the oak, and then either bottled or bulk aged in stainless steel tanks. This time is normally determined by the newness of the oak, the newer the shorter time needed.
You can cold stabilize with oak present, but the extraction will slow down with the cooler temps. Cold stabilization is best achieved earlier. I usually stabilize mine as soon as they have cleared, and before they are put over oak. The beauty of using carboys is that you can stabilize the wine, then put over oak, and when it tastes right, remove the oak and continue to bulk age. This is more of a hastle when using barrels.
You have a choice that you have to make, either stick to your timetable for bottling, and maybe not have the desired amount of oak, or delay the bottling until there is enough oak. Oaking doesn't follow a formula, it is strictly by taste. Soooooooo...bottom line is that the choice is yours. Who knows, you might actually get lucky and have the amount of oak you want at the six week point, ready for bottling.
Next time, though, add the oak early, remove at the right time, and then bulk age or bottle.
because you are just adding oak, also remember that the tanins in the oak will need to lay down, so considerable ageing will be needed of this wine due to the late addition of the oak. It will still need another year of either bulk or bottle ageing before the tanins start to lay down.
Good Luck!!