Yes, you are supposed to be able to train a model on one dataset, and then use that model in a different dataset without having to add decoys, train, etc.

If this did not work for you, then it is likely that your second dataset is missing one or more features that were available in your first dataset. (The error you would see is "Failed attempting to reintegrate peaks. The current peak scoring model is incompatible with one or more peptides in the document. Please train a new model."

In your second dataset, you can figure out which feature is missing by going to:
Edit > Refine > Reintegrate
Choose "Edit List" in the dropdown
Then select the model you want to use and choose "Edit".

Then, in the Edit Peak Scoring model dialog, you should be able to see which feature it is which is missing from your dataset. The missing features will be gray and italic, but will also have a non-zero value in the "weight" column.
You can click on one of these missing features. Then, switch the tab to "Feature Scores". There will probably be a bar in the bar graph labeled "unknown". If some but not all of your peptides are missing the feature, then you can hover the mouse below the "unknown" bar and a binoculars button will appear, and if you click that, then Skyline will list all of the peptides that are missing that feature will get listed in the Find Results window in Skyline.

If only a couple of peptides are missing that feature, then you might want to remove those peptides from your Skyline document so you can use the model you already have. Otherwise, you might want to go back to your high quality dataset and train a new model, but be sure to uncheck whichever features are missing from your low quality dataset.

Here's a page where we talk about reasons that the "Library Dot Product" feature might be unavailable:
https://skyline.ms/announcements/home/support/thread.view?rowId=37393

-- Nick