She could be picky, try different foods, or perhaps she is still adjusting to her new environment, I've had bettas that would not eat a few days after I got them. Changing homes in stressful for them.
as for her not eating because she wants to breed, I don't know, some fish will reduce appetite when their eggs are mature. I am not sure if bettas exhibit this behaviour.
As for breeding I would research like they said. Maybe take a few months or so that'll give you enough time to pick out the perfect male
It costs a lot to breed as well, because you need extra tanks and whatnot so you may need to save money anyways while you are researching. To tell if she does have eggs look at her belly, is it kind of swollen or full looking? She will also have a little white thing sticking out on her belly, that is her ovipositor which is where the eggs would come out, if you can see this she is mature enough to produce eggs. Also if around a male she will get dark vertical stripes on her body. If you see stripes and they are horizontal...those are stress lines which means something in her environment is bothering her.
If you do get a male (or have one already) you can set their tanks beside each other, it is fun to watch them flirt! :)