I used to use one in Indonesia but not here so cannot recommend a network supplier but it did work for me downloading movie torrents. Cost will be based on data usage. Where you get the actual device in Phuket i don't know. But in theory any local mobile phone shop should have one. For reference On Lazada the devices are between 1600 and 2400 baht.
Depending what you do for work speed maybe an issue.
Yes I believe AIS has data only SIM but all networks probably do.
Using you phone as a hotspot will work but uses a lot of battery.