NOTE: Before booking any sort of lodging, read the reviews first before committing. To get reviews, copy and paste the name of the cottage/B&B/apartment/camp site onto Google and most likely you will be able to find a Google, TripAdvisor (http://www.tripadvisor.com) or UKCampsite (http://www.ukcampsite.co.uk) review. You also need to review the terms and conditions of each accommodation. This info can be found on the booking site or each individual website.
If you have a child under 2-years-old, most are free of charge. If there is a fee, it'll be £5 or so. Not much. Some places may even have a cot and high chair for you to use. But free or not, you still need to let them know that you'll be bringing one (or two) for safety and fire regulations purpose.
When doing a search, let's say for a group of 4 adults, 3 children over 2-years-old and a baby, put in 4 adults and 3 children in the search criteria. Once you see one you like, scroll down or to another tab with the details and read the baby info. If all's good, book it and in the notes section inform them of the baby. If you're not sure, ring them up!
http://www.cottages4you.co.uk (Used this company many times and the cottages are as advertised and reviewed. Great when renting in France owners tend to speak English since cottages4you is a UK company. Some even have UK satellite service.)
The below link takes you to dog friendly cottages (although if you use the search function on any of the above link and make sure "pet/dog" is checked):
If you are leaving the island, make sure you read the how to take your pet(s) in and out of the UK. Your pet will need a pet passport and the base vet at Feltwell can get one for you. It does take a few weeks so do plan ahead:
