I'm considering to use CCR1036-12G-4S to route about 2Gbit of traffic (200-300k pps). Because it does not have a 10G port, I'm thinking to use 802.3ad to aggregate two gigabit ports and connect to a switch.

Has anyone tried link aggregation with cloud core router? Is it stable?
How does CCR perform for simple/queue tree on aggregated interface?
Do all 36 cores utilise if two gige ports are in use only?

I appreciate any input.

I think is not stable. I have issue in queue.

LACP is working great, use L3 hashing to properly aggrogate traffic across both links.

As for QoS, if you want to use all 36 cores, use at least 16 top-level queues and it will work.
You can find more info about this in v6 presentation from this year's US MUM.