We camp lots with babies and toddlers. it's no worse than any other sort of holiday with them
And can be better. They usually love it, often sleep better than indoors, and have lots of space to run around. we never use a travel cot, just snuggle up to them to keep them warm and happy.
I'd suggest making sure you have waterproof cagoule suits and wellies if the baby is mobile, especially for a crawler who will get soaked in wet grass otherwise. Lots of warm clothes, obviously. Campsites with washing machines and tumble dryers can be well worth it.
Breastfeeding little babies helps a lot. For sterilising anything, use tablets (from Boots and other places) rather than trying to take sterlisers or boiling water for ages.
Other things we've found useful - you can construct a "babygym" easily with a rope and a few toys on clips to amuse a young baby, or hang things off a guy rope.
also, maybe expect to cook less than you would normally when camping - check out local pubs and cafes, get takeaways, etc, anything to reduce the workload.