Is it legal to put an infant seat in a street legal golf cart?

I do not have a car and want to avoid property tax, registration, and inspection stickers that come with a car. I only would need to go short distances such as a mile to the grocery store, a forth of a mile to my stepdaughters school and maybe even 3 miles to the nearest walmart. My baby is only 5 months old and would need to come with me. Is it legal to put her seat in the cart so she can come along? Also can my 5 year old ride in the cart too?