ok, pretty much any of the luxury hotels in Dubai will be just ok budget-wise assuming you are sharing a room with your dd.
The best ones for kids are probably the Ritz Carlton and the Royal Mirage. Both are a bit lower rise than most in Dubai, have kids clubs that you can go to with your dd (I have found that even if we don't want to leave ds alone in a creche it is quite useful to have a place with loads of toys and activities we can go to together. Often this will be if dh is having a spa treatment and vice versa when I have one!)
Both have pools and private beaches.
Royal Mirage has a lot of different restaurants.
Dubai versus Mauritius is an interesting comparison as Dubai is much more built up, although obviously closer. Time differences very similar, flights much longer to Mauritius but as someone said, they are overnight whereas even if you take an overnight flight to Dubai the flight is too short for dcs to get a proper sleep. Do you think your dd would sleep on a plane?
Note that not all flights to Mauritius are overnight - I don't know about ones from Paris.
Loads of stunning hotels in Mauritius within budget. The Residence and Telfair come to mind as very child-friendly if you want to take a look. Paradis and Dinarobin too.
All five star, pools, beaches and fab spas!