Ahem. Around here, we call that "in good weight" or "in good flesh", not fat.
Nothing about that mare's photos make me think she's in foal.
However, if she had been bred in April, May or June, the times accidental breedings are most likely to catch, she'd hardly be showing now anyway.
If she's been exposed to a stallion, have a vet check her. Same if you recently acquired and you have no idea about her stallion exposure. If she's been under your supervision for the last 10 - 11 months, and there's no likely "baby daddy", I wouldn't worry about it.