Migrate Wodpress site from .com on one server to .com.au on a new server

I need someone to manually move my .com domain from one host to my new .[login to view URL] domain on a different host server. I have already tried using the 'duplicator' plugin for Wordpress, but it doesn't work because my host server only allows a maximum 120second timeout which causes duplicator to always fail, hence the need to manually move everything across. With regards to the SIZE of the project, it is very small because we only have 1 Wordpress template, 15 portfolio products and 2 blog articles. Total .ZIP file came to 69Mb only. Need someone who has done this many times before. Please do not apply for this if you have no prior experience. Thanks.