shop - shopper, run - running, swim - swimmer, cat - catty, pet - petted

Notice shop / run / swim / cat / pet have 1 syllable, 1 vowel next to 1 end consonant (1:1:1). When this happens, we double the end consonant with vowel suffixes (-ing, -ed, -er, -est, -en, -ish, -ery, -able, -y). 'y' is sometimes classed as a vowel especially at the end of words.

shop - shopper, shopping, shoppable, shoppability (but not shops because we only double up with vowel suffixes)
run - runner, runner-up, running, runny
swim - swimmer, swimmers, swimming
cat - cattery, cattily, catty, cattiness
pet - petting, petted
slim - slimming, slimmed, slimmer, slimmest
fat - fatter, fattest, fatty, fatted, fatten, fattening

quiz & quit
qu is classed as one consonant sound because we can't have 'q' without the 'u' in English words. So quit and quiz have 1 syllable with 1 vowel next to 1 consonant
quiz - quizzed, quizzing, quizzer, quizzical, quizzically
quit - quitter, quitting

But we never double up words ending in h, j, k, q. v, w, x, y
grow - growing
box - boxer

This doubling up rule was put into place centuries ago to indicate the short vowel sound, so we don't get them confused with long magic 'e' vowel sounds when we drop the 'e'. Knowing this helps not only your spelling but reading too. For example,
hop / hope
We use the 1:1:1 doubling up rule for hop - hopping, hopped
for hope we drop the 'e' when adding vowel suffixes = hoping, hoped

short vowel sound / long vowel sound
strip / stripe
stripped / striped
stripping / striping

short vowel sound / long vowel sound
tap / tape
tapping / taping
tapped / taped

short vowel sound / long vowel sound
slim / slime
slimming / sliming
slimmed / slimed
slimmer / slimier (slime - slimy - slimier)
slimmest / slimiest (slime - slimy - slimiest)

For doubling up longer words Click here to go to the Shorty Doubling Up Longer Words lesson