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It is simply impossible for anyone here or anywhere else on the internet to give you any useful advice regarding the specifics of your vehicle. Any car that is more than 20 years old and has 270,000 is going to be at a higher risk of having a break-down, but the only way to know if your vehicle is likely to make it or not is to have a very complete inspection done by a good mechanic. Without physically seeing your car its just impossible for anyone to have any idea what issues you might face.

We can tell you that roadtrip miles are easier on a vehicle than the stop and go of LA traffic, but if you do have a breakdown, getting it towed and/or fixed in the middle of desert could be quite expensive. At the very least, I'd recommend having AAA or some other breakdown coverage.