@Natalie ********
>1) currently inside Thailand
You may be getting a single entry Non-B visa inside Thailand. They are somewhat difficult to get, and will let you stay for 89 days. Generally the business name is written on this Non-B visa, and you can't jump to another employer.
>2) She is 3
EVERYONE in Thailand should have the proper visa and extension of stay. Children under 15 years old are not fined or have any other punishments for being on overstay, but if you are planning on enrolling her to a school, they may want a proper visa.
>3) I was told she would go onto a non-o visa based on being a dependent
That's correct, but there's no fine or punishment for children under 15.
>4) so if I get my non b visa (I don’t yet have a work permit) does this mean I could get a job at a different company than the one who I have already accepted a job with?
Probably not. I'm almost certain the Non-B will have the employer's name written on the visa stamp.