All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Paying Mahr (bridal-money) is compulsory; it is even an integral part of a valid marriage by the command of Allah; Allah Says (what means): {And give the women [upon marriage] their [bridal] gifts graciously.} [Quran 4:4]
There are no restrictions on the amount of Mahr, such as minimum or maximum Mahr, in Islamic Sharee’ah. Even though being moderate in demanding Mahr and not asking much Mahr, considering the financial condition of a marrying person, is recommended in the Sharee’ah. Therefore, asking a small Mahr and making the marriage ceremony easy for the future husband is highly commendable in Islam. In addition, making Mahr easy is a great way to reduce spinsterhood in society. The Prophet said: “The most blessed marriage is one which is held with the least expenses.” [Ahmad]
Anyway, pay a Mahr as much as you can depending on your own abilities. You may pay her only one dollar if she is content with it. But, without Mahr marriage becomes invalid.
Allah knows best.