In the concrete case, it makes no difference whether " or ' is used. In both cases doas is interpreted as a string.
With variables, for example, the situation is different:
echo "$HOME" returns the current home directory, while echo '$HOME' returns the string $HOME.
echo "doas" and echo 'doas', on the other hand, return the string doas in both cases.
edlin@Devil:~$ echo '$HOME' "and" "$HOME"
$HOME and /home/edlin
edlin@Devil:~$
edlin@Devil:~$ echo 'doas' "and" "doas"
doas and doas
edlin@Devil:~$
My entry in ~/.bashrc is alias sudo="doas ". The check returns
edlin@Devil:~$ alias
alias ls='ls --color=auto'
alias sudo='doas '
edlin@Devil:~$
edlin