I've got a huge sweet tooth. I love sweets and candies. Here are my picks for Peruvian sweets that you've got to try.
Alfajores
From http://blog.goway.com/agent/2013/08/recipe-alfajores/
Manjar blanco (which is similar to caramel) is sandwiched between two butter cookies and the whole thing is sprinkled with powdered sugar. If you're in Peru, you can buy manjar in a bag. It's addicting. I could eat it straight off a spoon. They cost about 1 sol or 2, depending on the size.I like mine without powdered sugar, since you can't claim not to have eaten all the alfajores when you have powdered sugar all over your chin and clothes.
Here's a recipe for powdered sugar alfajores and recipe for chocolate ones. The chocolate ones are more common to Argentina and Uruguay, so if you want the real Peruvian version stick to the powdered sugar ones.
From http://twicsy.com/i/NZxiXc
Besos de MozaLiterally translated it means, "the waitress' kisses". They have a graham cracker bottom and are filled with merigue and the whole thing is dipped in chocolate. They cost about 50 centimos. I love them! My all-time favorite dessert is a toss up between besos de moza and chocotejas.
I've been told these are originally a German dessert, but since they've been in Peru for over 50 years and I love them, they get included in this list. There are three flavours: vanilla, strawberry, and lucuma. Of course vanilla's my favorite flavor and the original one.
Here is a recipe for vanilla besos de mozas. The recipe's in Spanish. If you don't know Spanish, you'd better get cracking. The two programmes I recommend are Synergy Spanish and Speak From Day 1.

From La Teja
ChocotejasChocolate and arequipe (which is dulce de leche, it's a bit thinner than manjar). Yum! Sometimes you can buy these in little stores and restaurants. You can also buy them off the street from cholitas. I personally prefer to buy them from the cholitas and so that I know all the money is going to them. They cost about 50 centimos or 1 sol.
As far as I know, these are totally a Peruvian invention. They're absolutely wonderful. You've got to try them.
You can put all types of things in the manjar, such as pecans, raisins, coconut, grapes, peanuts, drunk raisins (raisins soaked in rum or pisco). Here's a recipe for chocotejas.

From http://great-peruvian-recipes.com/leche-asada.html
Leche AsadaIt's made of regular milk, eggs, and sugar. You can also add evaporated, condensed milk, vanilla, and cinnamon. It's a type of custard and it usually cost a couple soles.
Asada in Peru is slang for angry, so this dessert literally means "angry milk". Asada also means grilled or roasted so carne asada is grilled meat. I prefer the slang version myself. According to some people it's a Chilean dessert, but we all know that Peruvians and Chileans have on-going arguments about what's theirs.
Here's a recipe for leche de asada. Be sure to try it out, it's a great way to end a meal.

From Peruvian Cuisine
Literally translated into "a woman's (from Lima) sigh" it has a caramel bottom and is topped with meringue and sprinkled with sugar. It's a very rich, sickly sweet dessert that's hard to finish by yourself, so enlist a friend.
The name alone tells you that it's a Peruvian dessert through and through. While you can easily make it on your own, the next time you're in Lima you should give it a try.
Here's a recipe for suspiro de Limeña. You can also add some liqueur to the recipe as well.