Hello Marie,
No need, everything is included for 108 prints.
Moreover, this printer does not use ink as such, but "cartridges" containing a film that transfers the colours onto the paper by heat reaction in four passes (cyan, magenta, yellow and top coat).
Each cartridge is calibrated for an exact number of prints, in your case two cartridges allowing the printing of 54 photos (or three cartridges of 36, I don't remember).
In short, no drying out of the ink or clogging of the print nozzles when the printer is not used for a while.
The refill kits will always contain the paper and cartridges for the number of sheets.
That's it.