Before you understand this, let me explain you one thing. Srimati Radharaniji is the head of the Gopikas. And Krishna didn’t marry Radha at the age of 11. What actually happened, as per the Bhagavata, is this:
Neela was the daughter of Kumbhaka, the brother of Yashoda, who had kept seven bulls. These seven bulls were demons in the disguise of bulls. Krishna killed those seven bulls and then married Neela. Neela had actually done penance to marry Krishna and become His first wife before His upanayana, or thread ceremony. So, to fulfill that, Krishna married Neela. This Neela later merged into Neela, or Nagnajiti, who was one of the eight ashtabhaaryas of Lord Krishna. At that time, Krishna wasn’t even 10. After that, the Dhenukasura and Pralambasura Vadha took place. After that, the Govardhana Uddharana Leela took place (then Krishna was 7 years old).
He performed the Raasakreeda when He was 8. He even married the Gopa Kanyas who did the Katyayani Vrata to get Krishna as their husband. These Gopikas who did the Katyayani Vrata were unmarried Gopikas. And Krishna married them. And out of those, Srimati Radharani ji was one who was the head of these Gopikas. These Gopikas had the presence of Lakshmidevi, and Sri Madhvacharya also states the same. So, Srimati Radharaniji as a Gopi, definitely has the presence of Lakshmidevi within Her. Plus, Krishna doesn’t even touch a thing without Lakshmi sannidhana, because He is a Patnivrata and doesn’t marry anyone except Lakshmidevi. Either one must be Saakshaat Mahalakshmidevi, or one must have Mahalakshmidevi’s sannidhana in them to marry Krishna.
Gopikas had that Lakshmi Sannidhana within them; therefore, Krishna married them. Plus, these Gopikas were Apsara Strees who had done penance to get the sanga of Krishna. Plus, these Apsara Strees have the explicit right to worship Bhagavan Vishnu as their husband. Bhagavan Vishnu also accepts the Apsara Strees as His wives when they have Lakshmi Sannidhana. So, they incarnated in Vraja. So, now, coming to why Krishna married Radha or other Gopikas at such a small age? Let me tell you that Krishna doesn’t possess lust or a feeling like, ‘Oh, I cannot live without them’ like this. Because He is Svaramana. He doesn’t even need Lakshmidevi for His ananda. He is full of ananda in Himself. He gives ananda to Lakshmidevi.
Krishna sometimes acts as if He is missing His devotees to show how much He loves them, and He does it to give pure ananda to the devotee, not because He depends on them. Krishna is independent. Now, let this be the stage for my answer. As I said earlier, the Gopikas were Apsara strees. They had done penance to marry Krishna. Therefore, they were born as Gopikas with the special presence of Lakshmidevi within them. They did the Katyayani Vrata to get Krishna as their husband. Now, Krishna already knew He had to go to Mathura to kill Kamsa and do the further Bhu Bhaara Harana kaarya, because He appeared for that only.
So, as the fruit of Katyayani Vrata, the unmarried Gopikas married Krishna. Krishna had actually blessed the Gopikas earlier, promising to give joy to the unmarried Gopikas by marrying them, even before Balarama’s marriage and His own Upanayana. Therefore, to fulfill the wish of the Gopikas, Krishna married the Gopikas at that age. SriMadhvacharya also says in the Mahabharata Tatparya Nirnaya:
75) Due to the boon given to them (gopa-strees) by HIMSELF earlier, even before Balarama and even before HIS own upanayana, Lord Krishna had great enjoyment during the nights; LORD is the chintamani that ensures fructification of all requests, and HE is verily without even a trace of inauspiciousness!
[Mahabharata Tatparya Nirnaya, Chapter 13 Kamsavadha]
So, there are people who say that ‘Krishna wanted to marry someone, married someone else’ and say ‘Adhoora Pyaar’ because He didn’t marry Radha. This is completely wrong, because Krishna even married Srimati Radharaniji (as Gopa Kanyas, having Lakshmi Sannidhana and who did the Katyayani Vrata), and even married Rukmini Devi and Satyabhama Devi, who were Mahalakshmi Devi Themselves. So, stop treating Krishna’s life as ‘Oh man! Krishna suffered a lot!’ and reduce the pastimes of Bhagavan to a simple chocolate boy lover. The Gopikas clearly knew Krishna as Bhagavan and are infinitely greater than us, and not merely lustful lovers. We are not even the dust of their feet.
But then Krishna left them…they were very sad about this. But they weren’t sad forever. That doesn’t even mean they forgot Krishna. They discussed Krishna’s pastimes and didn’t curse Krishna for leaving them. There is one incident in the Bhagavatam: Krishna disappeared during the raasaleela because the Gopikas grew arrogant, thinking, " We are the luckiest women in this universe. And then, when Krishna disappeared, the Gopikas cried sweetly and called Krishna. Krishna came back.
The Gopikas asked Krishna, ‘Why did you disappear from us?’ to which Krishna replied, ‘To obtain something very special in your life, you have to value it. But if it is always with you, then you lose the value of the thing. When it goes far away from you, you come to know the value of it. So, to make you know this, I went away.’ So, Krishna wanted to strengthen the devotion of the Gopikas more. The more Krishna is away from the Gopikas, the more viraha and devotion would increase, and at the peak of that devotion they would see Krishna. That’s why Krishna didn’t come back to Vraja and directly meet the Gopikas during the Surya Grahana, before the Kurukshetra yuddha.
Hope this clears your doubt!
Jay SriRam!
ShriKrishnarpanamastu!