Yes.

"Tier" would be an animal of sorts. "chen" is a common suffix for cutiefying something or indicate it's small (and adorable).

"Tierchen" would be a cute animal, usually a small one too.

The suffixes "-lein" und "-erl" function similarly but have been largely replaced in common german (though in southern germany, both are alive and well)

The linguistic term for what you are describing is "diminutive".

I assuem that's the "-lein" in "Fraulein"? Is "-erl" the masculine version?

Hmm, interesting to try and pinpoint the difference between "lein" and "erl". I would say they are both diminutive but not exactly in the same way.

erl ... would be more related to the actual size

  Sack -> Sackerl (bag -> small bag)
  Wagen -> Wagerl (cart -> small cart)

lein ... would be more related to the inner size (sorry I can't frame this into words any better)

  Frau -> Fräulein (Woman -> Younger/Fragile woman (unmarried))
  Wagen -> Wäglein (Cart -> smaller but also lesser cart)

edit: referring to the answer of pavel_lishin. Yes "qualitative" modifier was the word I am looking for.

"erl" seems to be a purely quantitative diminutive, whereas "lein" seems to be more of a qualitative modifier, I guess?

It is the "-lein" in "Fräulein", but "-lein" isn't only for feminine nouns: the word "Männlein" also exists. I suspect "-erl" is the same, though I don't speak a dialect where it's used; some dialects have "-l" or "-li" which can also attach to any gender of noun (as in "Hansl" and "Gretl")

Awesome, thanks!