I have designed a LAB of 5 computers which are not connected to ant switch or hub in which i want two routers.

|HOST A |----|ROUTER 1|-----|HOST B |------|ROUTER 2|-----|HOST C |

HOST A
eth0: 10.0.1.192
HOST B
eth0: 192.168.1.19
HOST C
eth0: 10.10.1.192
ROUTER 1
eth0: 10.0.1.1
eth1: 192.168.1.1
ROUTER 2
eth0: 192.168.1.192
eth1: 10.10.1.1

WHERE all connections are using crossover wire.
what i want to ask is that can above designed configuration is correct?
can it be giving a simulation as i am sending a packet from host A to Host C
which is going through 2 routers in (consider) internet?
Also what should be Gateway addresses for each host for each NIC cards?
I am confusing what gateway address should be given to each host?

According to your diagram, host b should have two IP addresses, but you only show one. What's the subnet/mask used between host b and r2?

According to your output, r2/eth0=192.168.1.0/24 and r1/eth1=192.168.1.0/24. If these two routers were physically connected to each other, that would be correct, but host b is in the middle. So you need to add another subnet in your design to accomodate the connections between host b and routers r1 and r2.
Example:

HOST A
eth0: 10.0.1.192
HOST B
eth0: 192.168.1.19
eth1: 192.168.2.19
HOST C
eth0: 10.10.1.192
ROUTER 1
eth0: 10.0.1.1
eth1: 192.168.1.1
ROUTER 2
eth0: 192.168.2.192
eth1: 10.10.1.1

In fact, for simplicity of naming your diagram, try:

h1----r1-----r2-----r3-----h2

As for the default gateway... host a and host c are simple; point the default gateway to the connected routers IP address. As for the multi-homed devices (r1/host b/r2), they will need to have either static routes defined for each network that is more than one hop away -or- you can enable a routing protocol such as RIP or OSPF so that these routes are dynamically added.

why host B requires 2 NICs? What i want to have simulation of Inetnet in my LAB. as i send packets from host A to host C it is going through 2 routers. For that i am desiging such LAB.

Also what is following diagram that you have given. is is confusing me as it shows 3 routers.

h1----r1-----r2-----r3-----h2

One more thing as i have limitations to be in Single LAB all those Hosts and routers are physically connected as given in my problem diagram.