Can you freeze carrots?
Yes, you can freeze carrots
Best quality within 10 to 12 months, depending on the kind.

Where these times come from. USDA FoodKeeper has no entry named "carrots". The 2 kinds on this page are the USDA entries that cover carrots, copied without change from Carrots, parsnips and Baby carrots. Each row in the table is one USDA entry; pick the one that matches what you have.
whole carrots
Up to 10 to 12 months
baby carrots
Up to 3 months
Blanch before freezing.
What the freezer time means
Freezer times from USDA FoodKeeper are about quality, not safety. Food kept frozen at 0 F (-18 C) stays safe indefinitely; what changes over the months is texture, moisture and flavour. Wrap carrots tightly, press out air, and label the pack with the date so the window above is easy to track.
Thaw in the fridge, not on the counter. Anything that thawed in the fridge can be refrozen, with some further loss of quality; anything left at room temperature for more than 2 hours should not go back in.
Storage habits that make the difference
Store leafy greens loosely wrapped in the crisper drawer, ideally with a paper towel to absorb extra moisture. Keep potatoes, onions and garlic in a cool, dark, dry place outside the fridge, and store potatoes away from onions since they spoil each other faster. Trim and wash vegetables just before cooking.
Can you freeze other produce: fresh vegetables?
Source: USDA FSIS FoodKeeper dataset (public domain). How we decode the data.