"a small child and a small bed"
Translation:pieni lapsi ja pieni sänky
Yes. Many Finnish words are loans from Swedish. They are pretty easy to recognise when you know that Finnish does not like consonant clusters at the beginning of a word (so "strand" becomes "ranta", for example). And that voiced consonants often become voiceless (g->k säng -> sänk_, d->t strand -> rant_). Finnish also likes its words to end in a vowel, so additional ones are often added to the end (like "y" and "a" in "sänky" and "ranta").
"Sänky" is common in all instances when you want to use "bed". It's a loan from Swedish (säng), and refers to the piece of furniture.
"Peti" has a more restricted usage. It's also been loaned from Swedish (bädd, which is of the same root as the English "bed"). It's more colloquial, and doesn't have to be actual furniture. It can be any kind of construction, like only a pile of blankets for instance, that someone (or a pet) lays on.
If you want to "make a bed" it's either "pedata" or "sijata (vuode)".
"Vuode" is a third option for translating "bed". If "sänky" is kind of the frame of the bed, then "vuode" is more like the pillow, mattress etc. that you use, i.e. all the "soft" parts. "Vuode" sounds more old fashioned than "sänky".