So im rendering HD 1080p at 300dpi.
Makes no sense to say a unit measurement 1080P HD and 300 dpi when describing things. First of all your not ever rendering DPI the setting is not dots but rather pixels so it should be called PPI. The transform between PPI and DPI is nontrivial, the target resolution you want is based on number of pixels not any per inch value. Second 1080P hd IS a resolution and 300dpi is conversion factor so thet would set the size of your image, however thats allost 99% certainly not what you wan't because you know how large your output will be, which you say is 438cm x 186 cm.
Now the thing you want to know is what kind of LPI metric your printer has, its the printers analogue to PPI for a printer thats usually about 1/10 or 1/5 th of the dpi value of the outputing printer (its a question of how many tones you want). Then you take a and calculate your target PPi with the formula
1-2.2*LPI*(your dimension in inches)
with a factor of 2.2 you get the absolute maximum quality your going to ever get, eeven then the quality difference beween 1.5 and 2.2 is neglible with 1 being perfectly acceptable. Remember you are PAYING for each pixel, and qute frankly doing jpeg compression does more to the downgrade of quality then difference between 1 and 2.2 (you might avoid exact 1 tough). This means that for a REALLY good quality printshop result thats NOT your average digital promtshop has a lpi of 100-150*
Now then it does NOT end here when you print big things then 300dpi becomes a bit over the top and even 150-200 dpi becomes sufficient roughly speaking 200 translates to the kind of inspection ranges you get with a monitor. See the range at where epoeple look at your image matters. So you can easily get by a 50 lpi image.
it will come out pixelated.
printing anything but solid color is by default pixelated or well the eqivalent of printing process anyway called rasterized. Anyway the only way to understand what it looks like is to PRINT the damn thing, so test print small sections whet the same printer as you intend to aim for or a calibrated hard proof printer (your print shop will have one)
*however you ALLWAYS get the same 300 dpi form a print shop as a guide no matter if their lpi is 60 or 240 (meaning a 2400 dpi printer MINIMUM)