The things that i should check if im going to travel that long are the cooling system, mechanical, electrical and the engine.
-check for any leak, reservoir, radiator, water pump, radiator hose, thermostat
-check the mechanical of front and rear wheel (tie rod, ball joint, power steering, bushing, bearings, shocks etc) have them grease and also dont forget the brakes, check the thickness of pads and any sign of fluid leak
-check the electrical connections inside the hood, the tightness of battery terminal, insulation of the wires, possible loosening of wires. if you have multimeter check the charging of alternator, at engine idle the voltage should be between 13.6 to 14.3 volts. If not the alternator may need replacing.
-check for busted bulbs (switch on the parklight, head light, signal light etc) i suggest you bring extra bulb if in case the bulb get busted during the travel.
-and now the engine, check the belts if you seen formation of cracks replace it, any sign of oil leak kung meron pagawa agad.

additional:
change oil, filter and fuel filter na din

and last dont forget to bring atleast 1gal of extra water for emergency purpose only.

let see what others will say baka may idagdag pa sila, lets wait

good luck