They had to develop from the ship of Star Trek: Enterprise to the Enterprise of The Original Series and that would not have been easy, given the ships were a million miles apart. They would have created a secondary hull, meaning that it would look a little similar to what Kirk was driving around in.
Interestingly, a plan was hatched to make a Starfleet Academy movie that would have included the ship from Enterprise and it would have been very similar to what was seen on TOS. Doug Drexler was involved in the design process and did create something that looked really good.
Next: An Andorian joins the crew