Convert string to date format that can be used in a craft.entries tag
You could do this:
{# Your date 2020-11 in atom format e.g 2020-11-01T00:00:00+01:00 #}
{% set departureDate = craft.app.request.getParam('departure') | date(&quot;Y-m&quot;) | atom %}

{# Your date + 1 month in atom format e.g 2020-12-01T00:00:00+01:00 #}
{% set untilDate = departureDate | date_modify('+1 month') | atom %}

{# Query between those 2 dates #}
{% set query = query.startsOn(['and','&gt;=' ~ departureDate, '&lt;' ~  untilDate ]) %}

Note that on the November the 25th for example, you'd only be querying 5 days of the month