According to SOWPODS (the combination of Scrabble dictionaries used around the world) there are 3 words with the pattern -Q---ERS. That is, eight letter words with 2nd letter Q and 6th letter E and 7th letter R and 8th letter S. In alphabetical order, they are:

aquafers

aquifers

squarers

According to SOWPODS (the combination of Scrabble dictionaries used around the world) there are 65 words with the pattern S-U---R-. That is, eight letter words with 1st letter S and 3rd letter U and 7th letter R. In alphabetical order, they are:

sauciers

saufgard

saunters

sautoire

sautoirs

scudders

scudlers

scuffers

sculkers

scullers

scullery

scumbers

scummers

scunners

scuppers

scutters

scutwork

shuckers

shudders

shuddery

shunners

shunters

shushers

shutters

skudlers

skulkers

skummers

slubbers

sluggard

sluggers

slughorn

slumbers

slumbery

slumlord

slummers

slurpers

sluttery

smudgers

smuggery

snubbers

snuffers

snuggery

sounders

southern

southers

spudders

spunyarn

spurners

spurrers

spurters

sputters

sputtery

squalors

squarers

stubborn

studfarm

studiers

studwork

stuffers

stuivers

stumpers

stunkard

stunners

sturmers

stutters

There are no two letter words beginning with Q, as Q is always followed by a U. Therefore the shortest word beginning with Q HAS to be 3 letters long and the only word that fits this description is "Qua". So, Qua is the shortest word beginning with Q.

internetters

abetters

abettors

begetters

enfetters

forgetters

pipetters

regretters

resetters

unfetters

upsetters

usenetters

betters

bettors

etters

fetterers

fetters

fretters

getters

jetters

letterers

letters

metters

netters

rhetors

setters

sweaters

vetters

wetters

whetters

doubleheaders

featherbedders

beheaders

housewreckers

mopeders

retreaders

beckers

bedders

beddors

ceders

checkers

cheddars

deckers

eppers

fedders

feders

headers

leapers

lederers

lepers

medders

neckers

pepers

pepperers

peppers

shredders

spreaders

steppers

threaders

treaders

trekkers

wreckers

countermeasures

counterpressures

decompressors

enamellers

fortunetellers

intercessors

nonprogressors

overpressures

predecessors

quarrellers

rockefellers

storytellers

accessors

addressers

aggressors

agressors

allegers

appellors

assessors

backstretchers

barrellers

bestsellers

birdfeathers

blasphemers

bookcellars

caressers

chisellers

comparers

compellers

compressors

confessors

cupbearers

declarers

depressors

displeasures

dissevers

drivellers

endeavors

ensnarers

expellers

expressors

forbearers

foretellers

forevers

gospellers

gruellers

howevers

impellers

impellors

impressers

indwellers

libellers

mcevers

obsessors

oppressors

pallbearers

pinfeathers

possessors

precessors

preparers

professors

progressors

propellers

rappellers

redressers

regressors

repellers

repressers

repressors

resellers

snivellers

successors

suppressors

supressors

togethers

torchbearers

trainbearers

transgressors

trowelers

undressers

untethers

whatevers

whoevers

yodellers

barers

bearers

beggars

bellers

bevers

blessers

blethers

carers

cellars

clevers

darers

demars

devers

dredgers

dressers

dwellers

ebbers

ebers

edgers

eggers

ehlers

ellars

ellers

errors

essers

etchers

evers

featherers

feathers

fellers

fetchers

fletchers

gethers

gregers

guessers

heathers

hedgers

heifers

hellers

jaegers

jeffers

leathers

ledgers

legers

leggers

lessers

lessors

lethers

levers

measurers

measures

megers

mellars

mellers

mellors

meserve

messers

messrs

mssrs

nemmers

nethers

nevers

parers

pleasures

pledgers

pressers

pressures

rebers

remmers

scarers

segars

sellars

sellers

sengers

severs

sharers

shellers

sketchers

sledgers

smellers

smethers

snarers

sparers

spellers

squarers

starers

stellars

stevers

stressors

stretchers

swearers

tellers

telphers

terrors

tethers

treachers

treasures

tremors

trevors

wearers

weathers

webers

wellers

wethers

yellers

zellars

hope this helps:)