Exporting a logo in illustrator (pixelated?)

Hello community,

I have created a simple logo for my aunt's website and I am having a hard time exporting it. Before I export, I create outlines for the text to make it vector, and then I go to export as > PNG > Save.

I know I am doing something wrong, just not sure what it is just yet. Even on mobile the logo looks very pixelated.

Thanks for your help.