If this sentence is to describe something you do regularly, then sentence number 2 is correct.
If the sentence is describing something that is not done all the time, then a better version of the sentence would be correct the first part of the sentence also -- changing it to, "What I am going to do at this point."
“What I am going to do at this point is go home and have dinner.”
“What I am going to do at this point is (to) go home and (to) have dinner.” (I added the “to” in parenthesis because it’s ok to leave it out when you say the sentence, but in reality, it’s supposed to be there.)
“Going home” is the present progressive tense of the verb, “to go,” formed by combining the verb “to be” (I am) with the present participle.
All of that will probably sound like gobbeldy gook to you and won’t teach you anything right now because you might not be ready for it yet.
I’ll try to make it simple for you.
Your sentences (above) all start in the simple present tense: “What I do…”
They should start in something called the present progressive tense: “What I am going to do.”
It’s still present tense; it’s just a special form of the present tense that is not the “simple present tense.”
I guess you can think of it as a sort of “planning” tense:
Begin your sentence with, “What I am going to do is…”
(Don’t adopt that term, “planning” tense that I used here. In reality, it doesn’t exist. I just made it up to try to help you understand “ing” verbs.)
The present participle – or the verb ending in “ing” cannot be used together as a matched pair with an infinitive -- or verb preceded with the word, "to."
“What I am going to do is...”
You have to use the infinitive form (just the verb, preceded by the word, “to”).
The same applies to the next verb in the sentence, “having dinner.” You can’t use the “ing” form of the verb right after, “What I am going to do” -- which is still at the beginning of the sentence.
Also, you can’t mix the two verb forms in the same clause. You can’t take two equal verbs and make one into an infinity form (the verb preceded by the word, “to”), mixed together in the same clause with a verb ending in “ing.”
Again, you don’t always have to actually say the word, “to” when using the infinitive form of the verb in a sentence, but technically, it is always there.
Leaving it out and not saying it means that the word, “to,” is “understood.” Eventually, it will all start to make sense to you, but for now, just remember to always use the same verb form when two or more equal verbs are used together in the same clause.