Do I need to be married to obtain a visa for living in Thailand with my partner and child?

You need to read older posts in this group. Many of them contain the best information you require.

You need to find out from your local Thai Embassy if they issue a dependent visa for a spouse and, if so, what visa you need to apply for (probably a Non-OA) to get one. You then decide if that's the route you take and get married.

I recommend that a Retirement Visa is the best for you and that you should obtain it from the Thai Embassy/consulate in your country prior to coming to Thailand. I say that because if you come to Thailand on a Visa Exempt stamp or tourist visa, then you will be unable to open a bank account in Thailand and a Thai bank is required to obtain such a visa while in Thailand.