Translation:The hamster is eating a small carrot.
does ce for masculine aspirated-h words remain ce (and not cet as would be the case for mute-h words)?
Yes it does, and it sounds [suh].
ce hamster = suh amstèr
cet homme = set om
This H is "aspirated". This means that it still is mute but it behaves like a consonant.
Other examples: le homard (lobster), le héros, and most words borrowed from another language.