We plan to make umrah our honeymoon after the marriage contract (akad nikah). Is this a good idea?

It can be a beautiful beginning, as long as you understand that umrah is an act of worship with its own limits. While in ihram, marital relations and anything leading to them are forbidden until tahallul is completed. So plan enough time together outside the ihram period, for example a few days before departing or after returning. A newly married couple is also still learning to understand each other, and the tiredness of travel can cause unexpected misunderstandings. Choose a package that is not too packed. If the wife may get her period during that time, learn the rulings early. With preparation like this, umrah can become a spiritual memory that binds your love together. See prohibitions during ihram.