How do I use a regex in a shell script?

I am trying to match a string with a regex in a shell script. This string is a parameter of the script ( $1 ) and it is a date (MM/DD/YYYY) The regex I'm trying to use is :

^\d{2}[\/\-]\d{2}[\/\-]\d{4}$

It seems to work, I tried it on several regex tests websites.

My shell code is :

REGEX_DATE="^\d{2}[\/\-]\d{2}[\/\-]\d{4}$"
 
echo "$1" | grep -q $REGEX_DATE
echo $?

The "echo $?" returns 1 no matter is the string I'm putting in parameter.

Do you guys have an idea ?

Thanks !