Well, just getting married makes you a family, technically. But yes, she probably wants to start a family pretty readily, as well.
We just have to remember that, by Japanese law (to my knowledge), they can't do anything of the sort until around when they graduate high school, since he can't marry until he's 18, and his 18th birthday won't be for four more years. Even though Anna will be 18 by the middle of her senior year in high school (several months before he's 18), her age is the less pressing matter, since girls can technically get married as early as 16 in Japan, so long as they have written consent from a parent or guardian (thank you ToniKawa for teaching me that! Though I kinda already knew that they had something to that effect before, it helped hammer it home).
And I have no idea if this story will stretch into their high school years at this time, but if it does... that's going to be several, several Volumes away.