Later, you can experiment with different levels of glue freedom. Your toddler may develop certain skills before others, so you'll want to watch her own unique development to know what to introduce next. For example, you can cut a piece of a sponge into a square about (1 inch by 2 inches) and put that inside a clothespin. Then pour some school glue into a shallow dish and let her use the clothespin as a handle to dab glue onto her paper with the sponge. When she gets the hang of that, she will be ready to start brushing glue onto paper with a paint brush or a sponge brush from a hardware store.
The last thing I would do is hand a toddler a 4 ounce bottle full of school glue. That takes practice. Start with the smaller bottle first (less mess) but do let her experiment with the amount of squeezing it takes to get out a dot versus a giant blob. Another option is to use the little squeeze bottles that are used for cake decorating since you can control the size of the hole.
Glue stick can be deceptive. It's not as messy as school glue but it's hard for toddlers to see how much they are applying, though there are some that are colored that help alleviate that problem. They also dry a little faster so by the time your toddler gets around to placing her collage materials, they may not stick. I can't tell you how many glue sticks my toddler has broken by extending it too far and then pressing down too hard. Still, give it a try and see how it goes. It's got a steep learning curve, but once your toddler learns how it works, it can be pretty great in the cleanup department.
If your toddler and glue are like oil and water, try using double sided tape or using contact paper (sticky side up) for those first collages. Use clear contact paper like this and then place another piece over it when she's done and hang in the window for a fun suncatcher or Christmas ornament like the one pictured here.