How would you say "At about 3pm, I eat lunch at the house" in Japanese?
三時ごろうちでひるごはんをたべます。

Question

Answer

はい、その訳で正しいです。

私は、３時頃に、家(OR　うち)で昼食(OR 昼ごはん)を食べます。

わたしは　３じごろに　いえ(OR　うち)で　ちゅうしょく(OR　ひるごはん)　を　食べます。

Your Japanese is totally correct.

Answer

You could say it like this:
午後３時頃、家で食べましょう（ごごさんじころ、いえでたべましょう）

Because it is PM, you can probably leave out "lunch" that's understood, unless you want to mention you are eating a specific meal, like sushi, soba, etc.