Firstly: 

The scholars differed concerning the earliest time when zakaah al-fitr may be paid, and there are several views. 

1 – That it should be paid two days before Eid. This is the view of the Maalikis and Hanbalis. They quoted as evidence the hadeeth of Ibn ‘Umar (may Allaah be pleased with him) who said: They used to give (zakaat) al-fitr one or two days before (Eid). Narrated by al-Bukhaari (1511). 

Some of them said it may be given three days before Eid, because of the report in al-Mudawwanah (1/385) according to which Maalik said: Naafi’ told me that Ibn ‘Umar used to send zakaat al-fitr to the one who was collecting it two or three days before (Eid) al-Fitr. 

This view was favoured by Shaykh Ibn Baaz (may Allaah have mercy on him) as it says in Majmoo’ al-Fataawa (14/216). 

2 –That it is permissible to give it from the beginning of Ramadaan. This is the view of the Hanafis and is the correct view according to the Shaafa’is. See: al-Umm (2/75), al-Majmoo’ (6/87) and Badaa’i’ al_Sanaa’i’ (2/74). 

They said: because the reason for giving charity is fasting and then breaking the fast, so if one of these two reasons is present it is permissible to hasten it, just as it is permissible to hasten giving the zakaah of one's wealth after taking possession of the nisaab and before one full year has passed.  

3 – That it is permissible to give it from the beginning of the year. This is the view of some of the Hanafis and some of the Shaafa’is. They said: because it is zakaah and they likened it to the zakaah of one’s wealth with regard to paying it in advance in all cases. 

The most correct view is the first one. 

Ibn Qudaamah said in al-Mughni (2/676): 

The reason why it is obligatory is the breaking of the fast, which is indicated by the fact that it is mentioned in conjunction with it. The purpose behind it is to make the poor independent of means at a specific time, and it is not permissible to pay it in advance of that time. End quote. 

Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allaah have mercy on him) was asked, as it says in Majmoo’ al-Fataawa (18/zakaat al-fitr/question no. 180): 

I paid zakaat al-fitr at the beginning of Ramadaan in Egypt before I came to Makkah, and now I am staying in Makkah al-Mukarramah. Do I have to pay zakaat al-fitr? 

He replied: 

Yes, you have to pay zakaat al-fitr, because you paid it before its time came. The phrase “zakaat al-fitr” is composed of two words, which explains the reason for the zakaah, which is breaking the fast (fitr).  

So zakaat al-fitr is mentioned in conjunction with the fitr (breaking of the fast) because that is the reason for it, and it is known that breaking the fast of Ramadaan occurs only on the last day of Ramadaan, so it is not permissible to pay zakaat al-fitr except when the sun has set on the last day of Ramadaan, except that there is a concession allowing it to be paid one or two days before. Otherwise the proper time for it is after sunset on the last day of Ramadaan, because that is the time when the Ramadaan fast is to be broken. Hence we say that it is better to pay it on the morning of Eid if possible. End quote. 

Secondly: 

It is permissible to give zakaat al-fitr to a deputy to pay it on your behalf through a charity or trustworthy people etc at the beginning of the month, so long as you stipulate to the deputy that it is to be paid one or two days before Eid, because the proper way of paying it is to give it to poor and needy people who are entitled to it; this is what is mentioned in sharee’ah, that it is limited to one or two days before Eid. Acting as someone’s deputy in paying it comes under the heading of cooperating in righteousness and piety, and there is no time limit for that. 

This has been discussed in the answer to question no. 10526. 

To conclude: Paying zakaat al-fitr one week before Eid is not valid, and you have to pay it again, unless you gave it to someone whom you delegated to pay it such as a charitable organization that will pay it at the proper time, one or two days before Eid. In that case you have done what is required of you and it is regarded as zakaah that is valid and acceptable in sha Allaah. 

And Allaah knows best.