Get the paperwork from your vet with health certificates Etc and you need to apply for an import license for your dog you should be fine don't listen to these naysayers.
All you really need to know is how to order food other than that I have found everyone kind of forces me to speak English so they can learn English. 🤷♂️
You can definitely get the work permit you need while you are married to a Thailand National. There is no need to switch your Visa at all unless they want to control you. A prime example of this would be you switching your visa to a work visa now they control your Visa status and if they fire you they can cancel your Visa status and they will use that to threaten you