Having moved here in the last two years I can certainly support Elbert's advice. We only brought six boxes of stuff with us and that was way too much.
On the pet side, I would warn you now that bringing your bird in will be much more complicated than the other pets. But in four years that could all change. Personally, I do not think that this climate is at all suitable for an English Bulldog. I have owned an English Bulldog and would never have subjected her to these conditions. In addition to that the level of veterinary care is limited and there is not even an xray available on the island. We did bring one dog, but left our elderly cat with friends in the UK because we knew she would struggle with the climate and the lifestyle.
We know a lot of people who have brought pets from abroad and had health problems with them here. Remember that heartworm and tick fever are very common here. If you intend your cats to go outside, be conscious that cats get regularly eaten by larger predators here - think boas.
The other thing I can advise you from our experience is to be prepared for the completely different way of life and doing things here. English is the official language of Belize, but things here not done in any way like they are in North America or England. You need endless patience, willingness to compromise on just about everything, very high tolerance for people's differences, a very open mind and a constant willingness to learn if you are going to survive and be happy.
We have seen a number of people come here in the short time we have lived here and not last.
One last thing that we were told before we came, which is very important to know. If you have any problems or issues, sort them out before you come here. They will be magnified by living here.
San Pedro is paradise for us and many others, but truly it is all about the attitude you bring with you.
AmbergrisCaye.com 
