Okay Deb, I better understand where you are coming from.
Don't use Softaculous, or Fantastico.
Do you work from a PC or Mac?
Have you ever installed software on your PC or Mac?
What you need to do can be described in a few sentences, but for you to get there will probably require some time.
1) Get Moodle 3.5 installed on your host, with necessary plugins. Do you know what "theme" you are using?
2) Get your current Moodle 1.9 updated to 3.5 using MAMP/XAMPP/WAMP.
3) On your new moodle 3.5, replace the MySQL database and moodledata folder contents with your MAMP/XAMPP/WAMP data.
4) Test everything.
5) Swap your domains old moodle with the new. If done correctly, this should take less than 5 minutes while your moodle is in maintenance mode.
I regularly do 1, 3, 4, and 5. But I have never done #2 because I regularly update my Moodles, so I have never made this big of a jump.
But these steps are pretty much what I would recommend. Before going further, however, maybe Ken and others can suggest a modification to my steps. There are many ways to approach what you want to do.
But, I forget, do you have a VPS or hosted server with TMDHosting? This will be a factor.
I assume that you have a Linux server, with MySQL. Verify.
What does the URL to your moodle look like? Is it www.domainname.com, or www.domainname.com/moodle?
(I am just typing while I think. You may have already answered these questions.)
This process will probably take at least two months, based upon where I see you coming from. And because 3.5 is not 1.9, some things will probably have to be done a little differently. Also, I'm a teacher, currently teaching this semester, so I am in and out of these discussion forums. Since I have never done #2, I am going to have to rely upon others to help. Along the way, you will be learning new techniques. Are you up for this?
Where I would start if trying to help you get an experimental version of 3.5 running on your TMDHosting system. This would then allow you to explore the differences between 1.9 and 3.5.