PART 1

yes agree AM life generally is good

for career progression:
since this is your 1st AM compliance, please stay for min total 2-3 years to avoid being seen as job hopper by next hire (AMs especially love to see stability in career - i guess due to nature of industry)

also, 2-3 yrs will be sufficient for you to pick up hands on compliance work (sfa/faa/outsourcing/aml/marketing materials/licensing/code of ethics)

the question to ask yourself before moving is, have i learnt sufficient so that in my next job, i am fairly confident of advising on the above topics when being asked by business

if not, try to get as much exposure.
also, build industry network at the same time.
when you work in big AM, snr management love to do benchmarking (what are other houses doing in terms of this policy/regulation??)

if you feel due to nature of your current business/setup, you really cant accelerate learning anymore, then you may leave after 2 yrs (this will be your reason for your headhunter. it is a compelling reason if it is true)

to help you in visualising ahead.
when you work in big/global AM, there are many projects. (may need to work with regional/global compliance teams; but usually dont need travel. do phone calls instead.)

gain your manager and snr management trust with your attitude , passion and reliability (i assume you love this line of work) to work in such projects. raise your hand if have to. the more responsibility you take, the higher you are giving your company chance to promote you or give you higher than average team member's increment.