First, goats are ruminants. A big belly means they're taking in a lot of forage - which should ALWAYS be the staple in a goats' diet. Forage is not really a good food source, and it requires a lot of cellulytic bacteria and water to ferment that cellulose into metabolites that goats can use. A yearling animal is going through a lot of physiological changes and their bodies change dramatically as they mature, especially through the first few years of life. A young animal appears drastically different as a FF, which looks different in her 2nd fresh, 3rd fresh, 4th fresh etc/ In the goat world, we call a large stomach 'capacity'. Big capacity is a good thing considering they're turning a large amount of generally poor quality foods into a liveable amount of energy. Goats (and most animals) do not deposit body fat in the stomach area, so a big stomach is no a 'fat' goat. They can deposit body fat there, but they deposit fat externally and would need to be absolutely horrifyingly obese to really have substantial belly deposits.
Alternately, a big belly *can* be the sign of a heavy load of worms but this is harder to determine because they are ruminants. Goats are highly susceptible to worms, however, so monitoring worms using the FAMANCHA method as well as fecal quality and getting regular fecal tests done is vitally important. You can either use your local vet to do a fecal float, or you can ship samples to this lab:
http://midamericaagresearch.net/
Has she been around an intact male goat within the last few months? What breed is she? Some breeds do not breed in certain months - most breeds are seasonal and will breed only during late summer/fall/early winter. Young goats Gestation is 150 days, and generally belly size doesn't start to change until they are in the last 4-6 weeks of pregnancy. It is accompanied by development of mammary tissue too, in this time . An udder on a first time doe will feel like a little handful of mammary tissue - if she is not developing an udder, you'll find teats but it will not feel like a little handful of mammary tissue when you palpate it.
The way to tell for sure is to wait until she develops a mammary and has a baby goat coming out of her, OR you can draw blood and send it off for pregnancy testing. Pregnancy testing is easy and cheap. The cost is 6.50 per sample, and you ship it to BioTracking for fast results.
http://www.biotracking.com/
