There is really nothing like DQ11. The "Tales of" series, "Persona" series, "Legend of Heroes" series are good/great rpgs but they have a different feel to it. Dragon Quest kinda... makes you happy playing it? (even though it has sad parts). It has a lighter tone, even though the world's fate depends on you. I would say perhaps the Atelier series is a bit like that (but not as funny).
My suggestions would be:
- World of Final Fantasy. This would be the closest to DQ11, very fun, turn-based strategy combat, lots of 'Pokemon' collecting, cute chibi chars.
- Ni No Kuni. PS4 remastered version coming tomorrow. Personally I don't like the combat much though, but the Studio Ghibli art style and Pokemon familiars are very nice. (Don't get Ni No Kuni 2 though, that one not good.)
- Atelier Ryza. Also coming very soon (Chinese ver next week, English Oct 29). Latest entry in the series, looks to be the most friendly (no time limit, easier crafting etc). I posted a trailer a couple of pages back, check that and wait for reviews.