The aqicn values are legit, they are from the Dubai Municipality.
However, they are 1-hr concentration raw data converted directly to AQI and presented as "near real-time" on aqicn.org.
Index figures like PSI and AQI have health advisories (Unhealthy for Sensitive Groups, Unhealthy, Very Unhealthy, Hazardous) but such advisories are based on the averaged/sustained 24-hr duration. ie 15 mins, 60 mins or even 120 mins do not have Health Advisories attached to them.
But with our SG haze experience in 2014/15, many of us Healthy Individuals have experienced quite a fair bit of symptoms like headaches, throat dryness etc well under PSI 100/AQI 150 Unhealthy threshold.
For your baby, I'd wholeheartedly advise you to follow the Unhealthy for Sensitive Grps breakpoints
It might be more useful to follow the 8hr or even 1hr thresholds as pictured below.
I just convert the following concentration ug/m3 into AQI for your reference. Then you can easily gauge and take note for your baby when it hits AQI 139 for 1-hr duration and AQI 89 for 8-hr duration.
The Conc to AQI calculator used
http://www.airnow.gov/index.cfm?action=resources.conc_aqi_calc
Unhealthy for Sensitive Grps
1hr > 51 ug/m3 = AQI 139
Unhealthy
1hr > 88 ug/m3 = AQI 168
Very Unhealthy
1hr > 201 ug/m3 = AQI 251
Hazardous
1hr > 338 ug/m3 = AQI 388
Unhealthy for Sensitive Grps
8hr > 30 ug/m3 = AQI 89
Unhealthy
8hr > 50 ug/m3 = AQI 137
Very Unhealthy
8hr > 115 ug/m3 = AQI 182
Zabeel Park is PM2.5. This is very unlikely to be sandstorm which deals with much bigger than even PM10 (and besides I googled and found that they are frequent in Summer time only when there are NW Shamal winds, and in Mar 2011 there was a major one that affected large swaths of Middle East).
Dust storms also do not not really PM2.5 range. There is a difference between sand storms and dust storms.
5-days detailed history can be seen if you click that double square icon. Jebel Ali is PM10 though. Can't confirm if PM2.5 is above this or below this though.
But it probably is not low.