losing a pet, no matter of their size or how long you were together hurts just as much if not more than losing a human friend, so it definitely is not trivial. you will and have every right to grieve for both your dog and guinnea pig.
Whenever a pet of mine passes away, i burry them in either my garden or at the graveyard by my late partner. I then place a plastic box over the top with a heavy pot of flowers on top to keep wildlife from digging them back up. that way they are still close by, with their passed friends and given a good send off.
if your guinnea was one of a pair, make sure to give the remaining one lots of attention and cuddles as it will be grieving too.... yes pets do grieve, i once had a gerbil squeek constantly for a whole week until i couldn't bear hearing him so sad and went and bought him 2 baby gerbils to care for. Only when he was introduced to them did his squeeking stop.