"Well then, let's eat!"
(for non-native english speakers)
Yoda from star-wars speaks with incorrect grammar and uses the German sentence structure. German existed before English and English is a Germanic language, and uses a lot of the same words.
in german, the sentence order is different, and would be very incorrect if translated directly in the same order. In English, the only correct way to say it is "I must ・eat・ a duck"
importance -> verb -> thing
i should go to school
it's time for me to play football
i have to feed the cat
not 'to play football it is time'
じゃあ in this sentence is an interjection, usually translated as "well" or "so".
I think じゃあ is actually a casual/spoken form of the particle では which in turn, as an interjection, is short for それでは. I'm not entirely sure how to explain the interplay between それ, で and は in that phrase, but all in all, it roughly means "with that being the case..."
In most anime I've seen, it get translated to "thanks for the food" and I think it's the best way to translate it. There's a philosophy in japan that says you should be thankful for the food you eat and not waste it, because "There are seven gods in a grain of rice". It means that nature and people have put their lives in the line just so you could eat a meal and you should be thankful for it.
Here is a pretty good explanation: https://www.tofugu.com/japanese/itadakimasu-meaning/
いただきます (apart from being a set phrase and therefore not necessarily flowing the same rules as usual) I believe does not literally translate to "let's eat". It is just a useful translation since the two phrases are similar in use (moreso than the literal translations would be.)
Adding to that, いただきます literally means "to (humbly) receive" and can be used in other situations too, usually as an auxiliary verb.
To answer OP's question, it's not necessarily weird to say いただきましょう, but it implies that you are asking others in your group for confirmation that they too agree with your decision to receive it, and doesn't carry any of the same meaning we get from the set phrase いただきま.