What can I do to get bone structure similar to the model in the picture? (photo)

Based on the photos you sent, it is hard to evaluate fully.  It appears that you may have a small chin and a chin implant would give you a less rounded look.  The model in the photo has a thinner jawline thus her chin appears more pronounced.

The model has a well defined and continuous jaw line and not just a nice chin. The animated smile will "cross " the Hawkins so one needs a defined line extending behind the chin to prevent this issue and improve the contour. 

It is difficult to answer your question with the limited pictures you submitted. A full set of full face views are necessary. You can submit them privately or schedule a consult with a surgeon who does this work.

You need an in-office exam to determine the best course of action especially without side photos.  However, you would appear to benefit from some careful micro lipo and a chin implant.  Seek out a board-certified Facial Plastic surgeon for a consult.  Best wishes.