The Q-drone brings either a Heavy Machine Gun or a Plasma Rifle on its two profiles both for 1 Special Weapon Cost. It has an average BS but the Mimetism skill means it is better at winning F2F rolls than first glance would appear. It is also a remote meaning it can be improved with the Assisted Fire Supportware program allowing it to have Marksman Level 2. This grants it Shock ammo and allows it to ignore the Partial Cover BS modifier. With the plasma template in particular this is a deadly option. In melee it's poor CC stat means it will almost always be better to use Electric Pulse and hope for a poor roll from the opponent (a 35% chance) than to try and fight it out.
The Q-Drone has a 360 Visor and Total Reaction on all profiles allowing it full burst in ARO. Most opponents will be cautious when engaging a Q-drone and look to take them out with heavy modifiers such as ODD or TO Camouflage.
Mimetism will help against shooting attacks. Drones are almost always better shooting than Dodging, if they have the option, because of the usual -3 penalty on Dodges and Change Facings that REM troopers suffer. A drone's Silhouette is vertically smaller than a standard trooper making it easier for them to take some kinds of cover, which they will need as they cannot go prone.
Having G: Remote Presence gives this unit a second Unconscious state. In effect, it takes one more wound than normal to remove them from the table. It also ignores the "straight to dead" effect of Viral and Shock ammunition due to having Structure instead of Wounds, preventing easy ways to prevent repair.
G: Remote Presence also grants Courage meaning it can always choose to not take a Guts roll.
This drone benefits from the Assisted Fire supportware program more than most since it will always be firing at a high burst.
Suppression Fire also benefits the HMG Q-Drone since it allows you to pick between the Suppression Fire profile for close range shots, or default to the Total Reaction from longer range attacks. Even the Plasma version can benefit from this as it applies a -3 to the attacker further stacking modifiers in your favor.
A model with Cover and Camouflage using Surprise Shot from withing 8" or outside of 32" will prevent an HMG Q-drone from shooting in response. Surprise Attack makes this even easier as do troopers with ODD or TO camouflage, Nimbus grenades, or MSV troops shooting through smoke. Remember that a Q-drone has ~20% chance of a critical on any given shot, so it is best to give it no chance.
If the situation allows it Direct Template attacks are a good tool against reaction bots. Either the drone shoots, likely obliterating the attacker but suffering the hit, or it dodges needing a 7.
Q-Drones are good in low order count lists or missions where holding ground is key. They are good in all Sectorial armies and the Shasvastii Sectorial in particular likes them as they often want to avoid ARO with their more vulnerable camouflaged units.
Resist the urge to place a TR bot in the highest, best field of fire. It can be out shot from longer range. It is best to pick a long field that the enemy has to approach through, but which still gives you Total Cover from most of the board. This is doubly true for the Plasma Rifle profile that is vulnerable to long range snipers. It can be better deployed watching your Deployment Zone and then moving up into a midfield position once the coast is clear.
The Q-Drone is a good reserve model to be sure you are counter deploying it against its best targets. This is especially true against enemies with many impetuous troops, who the Q-drone will happily mow down before the active turn even begins.
Against camouflage heavy lists, it is also nice to have another trooper watching the same area as the Q-Drone so that it can hold it's ARO while the trooper Discovers any advancing Camouflage Markers.
If you are bringing a Q-Drone, it is best to accept that those points are already dead. At worst, your enemy will have to spend one order to remove it. At best, they will spend a dozen losing models to do so. Accepting that they can be lost trivially will help in playing the rest of your list.
Active Turn Role
Q-Drones can be used on the active turn to win fire fights with weight of fire, especially with Supportware. In general they are an ARO piece and should only look to engage enemies on the Active Turn if the odds are well in their favor.
ARO is the real purpose of these drones. As noted above it can sometimes be best to put them Suppression Fire just to have the option between different weapon profiles. Be sure to count modifiers before declaring that you will Shoot. Enemies with TO Camouflage or ODD can easily make it so that you have not shot.