Do you have joint residency, or are you the main carer of your daughter?
If your daughter will be away during a period where your ex husband usually has contact, then of course permission will be needed.
I take it that you don't have a very good relationship with your ex husband? if not, these things can be a nightmare. If you do get along ok then just let him know that you are away for a week..and that alternative contact can be arranged.
i had joint parental rights with my ex-husband but when i wanted to apply for passport for my 2 children i needed a letter from him to say it was ok and he gave full permision to take the children out of the country. i also had to do the same for him when he wanted to take the children abroad on holiday. this was when children were put on our passports though but i would imagine it to be the same - a letter of consent.
If you have a Residence Order for your child/ren, you can take them abroad for up to a month without the consent of anyone else with Parental Responsibility.