That all depends on what you paid for. If you paid for the standalone Office 2019 then you should be able to install that. If you paid for a 365 subscription, then that's what should install. Microsoft doesn't FORCE you into either. If you don't want a monthly subscription payment, then buy the full Office 2019 and pay once. Personally I prefer the subscription, but to each his own. It's the same software, for the most part.

I have Office Professional Plus on my desktop, but can't figure out how to get the entire setup file onto the laptop so I can install it there.

I'll be honest, it's been a while since I've done that. I've been an Office 365 subscriber since they started offering it as a monthly subscription back in 2011. Before that I always got Office on CD/DVDs. I'm sure there's a way for you to download the install MSI from Office.com no?

If its there I don't see it

Not sure. I'd suspect they have an option to download the install EXE, but like I said, I've been a subscriber for the past 10  years, so I haven't done this in a long time. Here's a help page. I'm sure if you paid for 2019 then that's what they'll give you. They're going to to force you into the 365 subscription.