If it's an internal corporate transfer they should be giving you full relocation expenses including the cost of a shipping container. $2,000 is about 7200 AED and that is half (minimum) of what a small 20ft container will cost. The contents of a 1-bedroom or small 2-bedroom apartment should be able to fit into a 20ft container.
If you have shipping included, it's best to bring your things with you as the cost of equipping a new apartment in Dubai can be quite expensive, even if you only buy the basics from Ikea. It's not just the furniture but all the little things such as linens, towels, small rugs, kitchen supplies, which quickly add up.
But there is no point getting shipping included if it's also not included upon your return to Chicago at the end of your contract.
35K a month sounds normal for someone in senior management at a PR
/ marketing agency. But it doesn't hurt to ask for more! You can easily survive on 35K with a nice lifestyle if you're happy with a 1-bedroom in a popular area or a 2-bedroom in a slightly less popular area only 10 minutes away. I can't tell you how easy it will be for your husband to find a job as it's dependent on his skills and willingness, but even if he only finds something for 15K a month, then as a childless couple making 50K a month you will be rolling in it.
This is what I would do:
1. Quantify your current expenses for your lifestyle in Chicago (your rent and the type of property it is), daily and weekly expenses, transportation expenses, socialization and any other costs. How much money are you saving at the end of each month?
2. Try to compare it to a similar lifestyle in Dubai. How much will you be able to save each month? (Use dubizzle to get a sense of property rents, with Downtown and Dubai Marina being relatively comparable to Lincoln Park or Lake Shore Drive).
Dubai may be tax free but you will not be receiving any payments towards social security or any other pension plans or able to contribute to your IRA accounts. Estimate the amount of lost employer contribution and deduct it from your estimated end of month savings in Dubai.
What is the differential? Is Dubai more expensive? If so, add that differential to the salary being offered. This should be your minimum starting point.
Is your initial package offer being structured as a lump sum package offer with no detailed breakdown? Or is it broken down into various subcomponents labelled housing, transportation etc cetera? The former is actually better for gratuity purposes as end-of-service gratuity is only applied to your base salary and not the benefits.
But is there assistance with housing expenses as rents are paid anywhere from 1-4 cheques a year, with about half of the landlords demanding one cheque for the entire year! You find a nice apartment in the Marina for 120,000 but it's in two cheques. Are you able to come up with 60,000 for the first cheque? Remember, there's a 5% agent's fee and a 5% deposit on top of that, plus deposits for your utilities and hooking up to the internet! Does the company offer any housing advance? Many companies do.
Regarding your pet, contact Dubai Kennels and Cattery for estimated pet shipping expenses. Their services include everything and all handling from picking up your pet to delivering it to you in Dubai. If you'd rather arrange for your own pet shipping with your pet as accompanied baggage on the same flight as you (this may not always be possible), contact Dubai Doghouse FZE as they know all the ins and outs of pet shipping and the required permits and costs. The difference between letting others do the shipping or handling the shipping yourself can be substantial, but the feasibility does come down to the type of pet and the country of origin. Please note that since you are staying in a hotel apartment for a month it will be next to impossible to have your dog with you as all except one hotel apartments do not accept pets. Even if you board your pet for a month before finding your own apartment, it may end up costing the same as having a professional shipper handle the shipping and flying the pet over after you've found your permanent apartment (ideally a family member or friend can watch your pet during that month).
Feel free to come back and ask more questions! I hope some of my suggestions didn't scare you. Many people come to Dubai for all sorts of reasons and are willing to accept a lower salary for the experience, while others are here strictly for the money. Some people are very happy to accept a situation that is financially exactly the same as back home, others demand a minimum of 100% uplift in salary and benefits. It's up to you to decide where you fall between the two ends.