The simplest approach is probably to just add 2500 to the existing IDs, since the target range (2500..3500) doesn't overlap with the existing range (2..600).
UPDATE qa_posts SET userid = userid+2500;
You could in theory set a random value between 2500 and 3500 like this:
UPDATE qa_posts SET userid = FLOOR(RAND() * 1001 + 2500) WHERE postid=42;
But you would need to do it for each post separately, or all posts would get assigned the same random value. Even if you do it separately for each post there will likely be collisions, i.e. some rows getting the same (random) value.
With that said, I don't think naïve approaches like the ones outlined above will work at all. The userid column in the table qa_posts is a foreign key, i.e. it references the column userid in the table qa_users, so you can't just insert arbitrary numbers. The IDs you insert must already exist in the table qa_users otherwise you'll be getting an error.
Updating a column in one table with random values from another table isn't all that simple, though. The SQL statements below would select the rows from qa_users in random order and then update the userid column of the qa_posts table with the user ID from the corresponding row in that randomized user list. However, that limits the update to the minimum of user count and post count, meaning that if you have 5 users and 10 posts, only the first 5 posts will get the userid changed.
SET @row1=0, @row2=0;
UPDATE qa_posts p JOIN (
SELECT t1.postid, t2.userid
FROM (
SELECT postid, @row1:=@row1+1 AS row
FROM qa_posts
) AS t1 INNER JOIN (
SELECT userid, @row2:=@row2+1 AS row
FROM (
SELECT userid
FROM qa_users
ORDER BY RAND()
) AS t
) AS t2 ON t1.row = t2.row
) AS u ON p.postid = u.postid
SET p.userid = u.userid;
It might be easier to fetch the user and post IDs with an external script and generate a series of UPDATE (or INSERT) statements from them, particularly if it's a migration task that will be run only a limited number of times. In Bash you could for instance do something like this:
#!/bin/bash
dbname='your_database'
readarray -t userids < <(mysql -u root -BN -e "SELECT userid FROM qa_users" "$dbname")
readarray -t postids < <(mysql -u root -BN -e "SELECT postid FROM qa_posts" "$dbname")
usercount="${#userids[@]}"
for id in "${postids[@]}"; do
rnd="$((RANDOM % usercount))"
echo "UPDATE qa_posts SET userid=\"${userids[$rnd]}\" WHERE postid=\"${id}\";"
done | mysql -u root "$dbname"
