why would you ever want a gamer laptop
just save up a little more and upgrade your desktop
Despite what people might tell you you're fine with this setup unless you're playing like 2020 AAA games on ultra settings or whatever. Just stick with this for another 2-3 years if you're not experiencing problems.
unless you are traveling a lot i see no points in buying gaming laptops since they are smaller, less comfortable, less powerfull and more expensive than their desktop counterparts.
i would go for a desktop if i was you but a stronger one since with a budge of 800/1000 dollars since 650 dollars isnt gonna be enough if you want to make your upgrade worth it.
don't get old gen cpu, go for a i5-10600k or a i7-10700k if you can afford it. For that gpu you would only need a 650w psu. I don't think you can afford all of htat with 650 bucks, as the psu is 100, ram is 60, tower is 60, ssd is 90, gpu is 300, mobo is 125, and that's already 735 without the price of the cpu. I would save up more to around 800-1000, especially if you need a monitor, and rtx 30 series should have more availability
1. You don't really need an upgrade(that's all up to you).
2. If you're going to upgrade, at least make it somewhat worthy....
I don't think what you're looking at is enough of an upgrade to be worth it.
At the moment I would suggest holding of on buying anything, the market for anything is overheated so prices on anything really good is hugely inflated - and you'll even have a hard time buying the parts at all.
As for gaming laptops, it is a matter of taste I guess only why buy an laptop unless you absolutely need the portability or don't have space for a full system. When buying a proper machine you can upgrade parts*, a great monitor will outlast stay great over several GPU's and ergonomics is better also.
*An example - I had a machine based on an early top end Core i7 CPU, that system stayed current with my swapping GPU twice, adding memory, adding disk space and so on... and when I build my self a new rig this summer I was able to carry over the case, the PSU, all the cooling fans and due to the crazy market for GPU's I am actually even running the old GPU(Fury X) while waiting for sanity to reemerge.