Could you implement a feature to set the toolip's font size?
In my UI it is very small compared to other LDB plugins.

Please provide a screenshot so I can verify exactly to what you're referring. I have to say, it looks the same as all my other plugins and I'm using a pretty high monitor resolution myself.

Sure, here are two screenshots one is from Broker:WorldQuests the other is from SavedInstances.
I'm using Chocholatebar as LDB addon, and TipTac fro tooltips.

Ok, I disabled TipTac and now all other tooltips appears as small as yours.
Just realized, that you are not using the gametooltip for the quest list, instead you created a separate frame.
So, is it possible to change the quest list's font size?

I looked into this and it turns out that the current "settings" for this addon is just one big "dropdown" (since it's just checkboxes and radio boxes). Therefore, to put in something more complex required to set the font size (an editbox or a slider, etc.) would probably require adding settings to the options->addOns menu.

I will see if I can find time to do this at some point, but it's honestly not that big of a priority. The text is still readable in the screenshots you provided, in my opinion and the default seems fine on my monitor/resolution as well (42" monitor running WoW at 3840x2160.)

Have you tried adjusting the "Render Scale" and "UI Scale" options in Options->Graphics? Also, if you're using a custom UI (like ElvUI) there might be a setting to change all the fonts at once. (The addon is setting a specific font type, but it's using the default font size.)