Can I book a ticket now if I'll have a new passport when I travel?

It will often be fine if you book now. However some airlines may ask for a passport number while booking the ticket.

The UK government says:

Don’t book travel until you have a valid passport - doing so is at your own risk. Your new passport won’t have the same number as your old one.

This doesn't mean you can't book now, but you need to take some precautions to make sure everything will turn out right.

For example, I booked a ticket with Aeroflot yesterday, and a passport number was required. Even if you book with them through a travel agency, they will send you an email demanding that you give them your date of birth, passport number, etc. Aeroflot may not be the only airline that practices this.

Since you are connecting in Dubai, it seems likely that the itinerary you are considering is with Emirates.

Emirates state on their website:

Emirates Skywards : Change of details

If you need to change your name, birth date or gender, please submit a help form. To change your date of birth, please attach your passport copy.

None of this applies to you, as it will all be identical in your new passport. However, it goes on to say:

You can edit any other information – including your nationality, passport number or passport country of issue – by visiting the Contact details page.

This applies to you if you fly with Emirates. You can keep your passport number updated with them using their website.

If another airline

If you fly with any airline that registers your passport number, that may cause a potential problem if you change passport after booking your ticket. Therefore, I recommend checking this before booking, and contacting the airline if necessary. Even if they do register your passport number, they may have a procedure for people who renewed their passports, or it might not even matter. This, however, is something it is good to know about prior to booking to avoid problems and inconvenience.