Yes, there are multiple flights from Great Falls International to Abu Dhabi International for under AED 4,775. The cheapest flight booked recently is on Multiple Airlines for just AED 4,506, but on average you can expect to pay AED 4,800.
There are no direct flights from Great Falls International to Abu Dhabi International, but Cheapflights can provide you with all the information you need to find the fastest route with the fewest stops.
When travelling, it's generally smart to pack in preparation for rain or any other conditions that may arise. The rainfall in Great Falls is roughly similar to Abu Dhabi. You can assume this to be the case over the next 9 days.
You can imagine temperatures to be in the 43 °C range in August. The weather in Abu Dhabi is generally hotter than Great Falls's. As flight availability is subject to become more limited as peak season approaches it is ideal to book in a timely manner.