I've been having various problems with Bing Google and getting my site to show up in search results. After ruling out just about everything else I can imagine I believe I've narrowed it down to the free registrar I used being out of compliance with Icahn or something?

So I went and bought a domain, now what I'd like to do is just replace everything straight across from my old domain to the new. I'm using WordPress so I believe I need to do the following:

Update the DNS for the new address to point to where my current site is. Can I point the new address at the folder that is my old domains name or would I rename the folder to the new domain? I'd imagine the latter if I'm running find & replace on my database a couple steps later? I'd like to avoid have 2 copies of everything if possible, the whole site is only a bit over 300mb but that would still mean going from 10% to 20% capacity.
Get an SSL certificate for the new domain so I'm going from https:// to https://.
Backup my WordPress installation and my database using at least 2 different methods.
Once the DNS change goes through update WordPress settings to the new domain.
Do a find & replace on a copy of one of the database backups so everything points to the new address.
Setup 301 redirects so any exterior links still go to the right place.

At this point everything should work right so I can log into Google & Bing Webmaster portals and verify everything there.

Am I missing anything? This seems too easy, like when I tried to move my site over here only to find out that my old host used some type of screwy character set or something in their .sql that no one had ever heard of and after 3 days I said to heck with it and just copy pasted my content over from a backup I had downloaded and the Way Back Machine. I REALLY don't feel like doing that again if it's at all avoidable.

Thank you so much in advance you guys have been incredible so far. Once I get this ironed out -- and myself in front of a pc instead of this #&$@ing mobile -- I'd be happy to do writeup for the tutorials section if you'd like?