If I cast spell queller and exile an opponents card, am I able to respond to the ETB with a flash speed emerge and sacrifice queller as the emerge cost thus dodging the leave the field effect? drownyard behemothor elder deep-fiend for example?
Yes. If Spell Queller leaves the battlefield while its enters-the-battlefield ability is on the stack, its leaves-the-battlefield ability will go on the stack on top of that ability (C.R. 405.2) and get to resolve before that ability (C.R. 117.4). But since its leaves-the-battlefield ability doesn't refer to an "exiled card", that is, a card exiled due to the enters-the-battlefield ability, when it would resolve (C.R. 607.2a), it will do nothing (C.R. 101.3).
EDIT (Dec. 25, 2019): Edited, including because one rule was renumbered with Core Set 2020.
EDIT (Jul. 31, 2020): Correct a rule citation.
EDIT (Dec. 25, 2019): Edited, including because one rule was renumbered with Core Set 2020.
EDIT (Jul. 31, 2020): Correct a rule citation.