Just a guess but the caulking around the base at the counter is probably faulty. The sink may be the problem over all. It will need to be mopped up around constantly and if your daughter isn't fastidious, it will be potentially leaking again. My thought would be to get a set in sink and possibly with an integrated backsplash to prevent water getting on the counter. A deeper sink would be more practical too, imo.

Yeah, this is more than "the faucet". It's a sink that looks good, but isn't designed to route stray water to the bowl. It's also calking on the backsplash / perimeter of sink that's not right.

Get a different sink that directs water that lands on the deck to the drain and a new faucet. While you have the sink out, fix the caulk.

I'd substitute a low-arc faucet that would drip into the sink but whose spout was not so high as to cause splashing. Example: Delta 3559-MPU-DST Trinsic Widespread Bathroom Faucet

Update, I called moen and they said that model of faucet had a known issue and has been discontinued and they sent me two replacements

Not surprised. No one beats Moen for customer service.