This cannot be done with a template, unless it is used in pages as
{{subst:Timestamper}}. (This might still be worthwhile if the template
is a bit more complicated than in your example.)
MediaWiki has a built-in syntax to generate a pretty timestamp: ~~~~~
(five tildes) – the output is something like "19:07, 6 September 2016
(UTC)". Perhaps your users can just use that?
--
Bartosz Dziewoński