Bathtub replacement cost

Recently bought a house is SoCal. The bathtub has a small hole (less than 1/8 of inch), which we patched with one of those patch kits. the tub also has dirty marks that won’t go away. We are expecting a baby soon and we don’t like to use the tub in it’s current state for bathing the baby, specially when she grows out of the infant plastic tub.

We have limited budget and I don’t want any other bathroom renovation at this time.

How much should I expect this to cost in SoCal? I thought to hire someone to replace the tub for me. I was thinking ordering a tub from floor and decor and hire a plumber for installation. Will bathroom renovation companies do this, without pushing me to do any other renovations?