You can develop everywhere you want. When you want to deploy, simply build the project on the Gentoo machine.
Note that you don't need to install Qt 5 manually on Gentoo. It is offered in the "qt" overlay. You add it with layman:
layman -a qt
Then you can emerge the Qt components you need by using slot 5. For example, to get Qt Core:
emerge -a qt-core:5
If you have never used Layman before, it's in the "app-portage/layman" package and you can find docs here: