Q: Should I take this car for a 3000 mile long trip?

Ultimately, you are the only one that can make that decision. I would suggest having a mechanic do a vehicle inspection before setting out on a long trip like this, as 3000 miles will pass some maintenance milestones. Having an inspection done before you set off should be able to identify any major issues that loom, and will give you a chance to get them repaired, which will at least lessen the likelihood of a breakdown. An inspection should cover belt status, major leaks, brake condition, hose health, fluid condition, and most of the overall condition of the vehicle. If this is something that you would like to have done, contact a certified mechanic, like those available at YourMechanic.com.