Do we still need to notify immigration within 24 hours when traveling within Thailand?

You need to ask the immigration office you deal with on what their policy is concerning in country travel.

Some say don't file a TM30 unless you come in from outside the country

Others are saying you need to file a new TM30 when you get back to your home even on in country travel.

If you're profile is to be believed and you're indeed in Korat, that'd be the office to check with.