Will you use this stroller immediately after getting off the plane?
飛行機 = plane
降りる = get off / disembark
すぐ = immediately
このベビーカー = this stroller
利用 = use
なさる = will/would you
日本で定員はとても丁寧な言い方がありますけど、もっと一般的に言えば、以下の例文になるかもしれません。
Are you going to use this stroller right after you get off the plane?
Would you like to use this immediately after the plane lands?
Between American, British, and Australian English, there are a lot of variations of names for the furniture that you mentioned. As a result, it may be easier for you just to say "this" and point at the stroller to ensure that they understand what you are talking about. I hope that this helps! :)
Will you be using the stroller as soon as you land?
When asking about the future we use the word 'Will' -- e.g.: 'Will you be landing at Kansai or Narita this Tuesday?' You could also say 'Are you planning to use the stroller when you land?'
未来について尋ねる時は、'Will'という語を使います。
例：
'Will you be landing at Kansai or Narita this Tuesday?'
（火曜日は関西国際空港に降りますか、それとも成田ですか）
ほかに、
'Are you planning to use the stroller when you land?'（着陸したらベビーカーを使いますか）
と言うこともできます。
Are you going to be using the pushchair straight after landing?
Will you be using the pushchair as you get off the plane?
In the UK we tend to use the word 'pushchair' rather than stroller although the person would know what you mean by both words
When asking if someone want to use something you would say
'are you going to be using?' or 'will you be using'
Landing or getting off the plane means the same thing
イギリスでは、どちらもわかってくれますが、ベビーカーのことを'stroller'よりも 'pushchair' と言います。
相手に何か使うことを聞くには、
'are you going to be using?'
（～を使いますか？）
'will you be using'
（～を使いますか？）
と言うことができます。
Landing や getting off the planeは着陸する、飛行機を降りるという意味です。
Do you need your pushchair/stroller when the plane lands?
Is the pushchair/stroller needed straight away after you land?
Both above would be good examples for you to use in the airport to ask your customer if they need the pushchair/stroller immediately. Straight away is another word for immediately.
Will you be using the pushchair when the plane lands?
Do you need to use the pushchair on landing?
You work at the airport, and, to a customer with a stroller/pram/pushchair, you want to ask them if they are going to use the stroller/pram/pushchair immediately after the plane lands.Any of the above suggested comments is suitable.
アメリカ合衆国 
イギリス 
