Untested, but try something like this:

$ua->post($url, 
    Content_Type => 'form-data', 
    Content => [
        field1 => 'value1', 
        file => ['data.txt'] 
    ]
);
[download]

Put any fields and values you need to post in there, and change file to the name of the upload field in the form.

I found this info in HTTP::Request::Common