You should be fine. And you should get at least 24hours of run time for you laptop if the battery is fully charged. Anything else you run off the inverter will subtract from that. If you were using the whole 300 watts then that battery would not last long. But the inverter will not use much unless you load down the output with larger current loads.
You also have all but one peice of what you need to have an everlasting amount of small power. You should look into buying at least a 5 watt 12 volt solar battery charger. With that you could keep charging your battery from the sun.
A marine battery is better for this situation because it is designed to be discharged in the manor you will be doing so.
As such it will have a longer life. But for the amount of time you will using the Car battery this should not be a big problem.
Thanks to all for excellent advice. My tractor batt. is dead, so I'll go charge it with car. One more question... I found 3 marine batteries but they're all dead. How long do I need to charge a marine battery with the car? About 15 minutes?
Will someone please ping the people who answered my invertor question? I would be forever grateful!!
Please send patches!!!