In a lot of areas in the country, the price to build is way too high to justify new construction to keep as a rental. Maybe if it's a modular or manufactured.
In terms of where to start getting estimates, call local building companies.
If you're a relatively new investor and don't have personal experience in home building, new construction is a pretty hefty way to get in the game...if you have enough money to build a new house, you might want to think about using it to buy existing rentals.
@Larissa Luna Your city planning/ building department is the first place I'd start. While it might seem obvious that a home will fit on the lot, you need to be aware of the specific zoning and building requirements for your lot. Setbacks and coverage ratios are just a couple of restrictions you will have to comply with.
@Larissa Luna It is doubtful that your zoning laws will allow a second building not connected to the original building on the same lot. As mentioned by Ken, ask your city planning/building department before doing too much research. Based on what other have stated on BP, you're likely looking at $125-150/ft2 to build low/middle end construction in California.
Additionally, a 6,000ft2 lot is not that large, and trying to fit another house on it would be a challenge, particularly with access and parking.