If you're *only* playing games on dolphin, anything much above a desktop geforce 750ti in performance isn't likely to be useful - that can do 4k in the vast majority of titles, which looks great if you use VSR supersampling to display on a 1080p screen. Similarly, having a faster processor than needed to run the most demanding parts of the game (or more cores, as mentioned above Dolphin itself doesn't really scale beyond 2) doesn't improve performance, FPS doesn't scale "up" like it does in most PC games, once dolphin can emulate a full-speed console it can't do any better.
If you only want 1080p and don't need lots of AA or similar enhancements, there are integrated GPUs that can pretty easily cover that (recent high-end Intel iGPUs or pretty much any AMD zen/vega APUs should probably do)
So if you plan to use your laptop as a purely dolphin-only machine, or only 'light' tasks like browsing the web and watching videos or writing documents, there's no need to stretch the budget.
One of the real questions with laptops is price range, and how much you're willing to sacrifice performance for the sake of size, heat and battery life. A good few machines boast high top-end specs, but lack the power delivery and cooling systems required to use them indefinitely, often throttling pretty hard. This likely means if you have a good looking laptop on the spec sheet, it may be worth trying to find reviews to make sure you're not going to be burned. This will likely mostly be an issue on the lower-end side of things, as the high-end likely has enough performance in the bag so that even if it throttles, there'll still have enough left to run dolphin without issues.
Pretty much any modern Intel or AMD Zen CPU in the "over 15w power" categoryshould be able to play the vast majority of games, if the cooling and power delivery can maintain that level indefinitely. Though be aware that if using the integrated GPU, the power (and heat) are shared, so you should probably bump up the bar accordingly.
Though be wary, as some very few games use features that are harder to emulate fast, so there's a few that struggle to play even on the current most expensive highest-power desktop CPUs, but the vast majority don't need anywhere near that level of performance - but be aware if one of your "must plays" happens to be one of those
