query regarding combining an update and an insert query into a single query in mysql
To do this without the risk of blocking another user trying to update the same profile at the same time, you need to lock the row in t1 first, then use a transaction (as Rolando points out in the comments to your question) :

start transaction;
select id from t1 where id=10 for update;
insert into t2 select * from t1 where id=10;
update t1 set id = 11 where id=10;
commit;