Can't comment on this specific incident, however a birdstrike on departure is not unusual for a commercial aircraft. Usually there's no damage and the aircraft continues en-route. Occasionally the crew will decide to return to the departure airport as a precaution. Very rarely, more significant damage may occur, usually an engine issue causing noise and excessive vibration, which will lead the crew to shut the engine down as a precaution. On a twin-engined airliner this isn't a huge problem in as much as modern twins have to be able to lose 50% of their power and still be able to maintain a certain climb rate. Before departure, all crews brief for certain situations - for example, they will always brief that if they lose an engine shortly after departure, they will climb to at least Minimum Sector Altitude [MSA], head to a certain bit of airspace, then run through their checklists and re-assess the situation. The MSA guarantees at least 1000' separation above the highest bit of terrain in that area, and almost certainly accounts for the 3500/3600' you describe.
So now, assuming they've shut an engine down and reached the MSA, they will have time to run through a load of checklists and decide on the best course of action. There are very few inflight emergencies which require an immediate landing (onboard fire is actually the only one I can think of)... the much safer option is for a crew to methodically work through checklists, plans, options, review... then act. Real life is not like the movies in that respect. Less exciting, more checklist based...and a lot safer as a result. It's not at all unusual for an airliner to encounter some kind of emergency like this, and then enter the hold for 20-30 mins or more before asking to make an approach.
Very few modern aircraft have the ability to dump fuel - another movie option - and so, unless it's a totally time critical issue [see above], some time spent holding will use up fuel and bring the aircraft weight down, enabling a slower approach and landing, which has many benefits.